This paper investigates two types of conditional strong law of large numbers (SLLN) under G-expectation, a non-additive probability measure. The authors introduce the concept of conditionally independent random variables and conditionally identical distributions within the G-expectation framework. They establish that the cluster points of empirical averages for conditionally independent random variables fall within the bounds of the lower and upper conditional expectations with probability one. Additionally, for conditionally independent random variables with identical conditional distributions, the paper shows the existence of two cluster points of empirical averages that correspond to the essential minimum and essential maximum expectations, respectively, with G-capacity one. The main results are derived using conditional Kolmogorov's SLLN and conditional G-capacities, providing a foundation for future applications in machine learning, reinforcement learning, and stochastic filtering simulations.This paper investigates two types of conditional strong law of large numbers (SLLN) under G-expectation, a non-additive probability measure. The authors introduce the concept of conditionally independent random variables and conditionally identical distributions within the G-expectation framework. They establish that the cluster points of empirical averages for conditionally independent random variables fall within the bounds of the lower and upper conditional expectations with probability one. Additionally, for conditionally independent random variables with identical conditional distributions, the paper shows the existence of two cluster points of empirical averages that correspond to the essential minimum and essential maximum expectations, respectively, with G-capacity one. The main results are derived using conditional Kolmogorov's SLLN and conditional G-capacities, providing a foundation for future applications in machine learning, reinforcement learning, and stochastic filtering simulations.