This paper introduces a sequential Monte Carlo (SMC) method for Bayesian inference without likelihoods, known as ABC-PRC. The method addresses the inefficiencies of traditional ABC algorithms, such as ABC-REJ and ABC-MCMC, which can be highly inefficient due to low acceptance rates and correlated samples. The SMC approach improves upon these methods by using a population of particles that are sequentially updated through a series of intermediate distributions, leading to more efficient sampling. The ABC-PRC algorithm incorporates a partial rejection control (PRC) mechanism to eliminate particles with low weights, thereby improving the efficiency of the SMC process. This method avoids the problem of "sticking" in regions of low probability and allows for more effective exploration of complex, multimodal posteriors. The algorithm is demonstrated through a toy example and an analysis of tuberculosis transmission rates, where it outperforms ABC-MCMC and ABC-REJ in terms of computational efficiency. The SMC approach is particularly effective in handling intractable likelihoods by using summary statistics and a sequence of intermediate distributions. It allows for dynamic adjustment of the tolerance level and provides a more efficient way to sample from the posterior distribution. The method is validated through simulations and real-world applications, showing its potential for use in various fields where likelihoods are intractable, such as population genetics and epidemiology. The paper concludes that the SMC approach offers significant advantages over traditional ABC methods, particularly in terms of computational efficiency and the ability to explore complex posterior distributions.This paper introduces a sequential Monte Carlo (SMC) method for Bayesian inference without likelihoods, known as ABC-PRC. The method addresses the inefficiencies of traditional ABC algorithms, such as ABC-REJ and ABC-MCMC, which can be highly inefficient due to low acceptance rates and correlated samples. The SMC approach improves upon these methods by using a population of particles that are sequentially updated through a series of intermediate distributions, leading to more efficient sampling. The ABC-PRC algorithm incorporates a partial rejection control (PRC) mechanism to eliminate particles with low weights, thereby improving the efficiency of the SMC process. This method avoids the problem of "sticking" in regions of low probability and allows for more effective exploration of complex, multimodal posteriors. The algorithm is demonstrated through a toy example and an analysis of tuberculosis transmission rates, where it outperforms ABC-MCMC and ABC-REJ in terms of computational efficiency. The SMC approach is particularly effective in handling intractable likelihoods by using summary statistics and a sequence of intermediate distributions. It allows for dynamic adjustment of the tolerance level and provides a more efficient way to sample from the posterior distribution. The method is validated through simulations and real-world applications, showing its potential for use in various fields where likelihoods are intractable, such as population genetics and epidemiology. The paper concludes that the SMC approach offers significant advantages over traditional ABC methods, particularly in terms of computational efficiency and the ability to explore complex posterior distributions.