The paper introduces MC+, a nearly unbiased and accurate method for penalized variable selection in high-dimensional linear regression. MC+ combines a minimax concave penalty (MCP) with a penalized linear unbiased selection (PLUS) algorithm. The MCP provides convexity in sparse regions, while the PLUS algorithm computes a continuous piecewise linear path of solutions. MC+ achieves high probability of correct variable selection without requiring the strong irrepresentable condition used by the LASSO. It also attains certain minimax convergence rates for regression coefficient estimation. The paper proves the selection consistency of MC+ under a sparse Riesz condition and demonstrates its superior performance in simulations compared to the LASSO and SCAD. MC+ is computationally efficient and avoids the computational difficulties of nonconvex minimization. The paper also provides a general theory of penalized least squares estimation, including the continuity of estimators, unbiased risk estimation, and noise level estimation. The results show that MC+ outperforms the LASSO in variable selection accuracy and computational efficiency.The paper introduces MC+, a nearly unbiased and accurate method for penalized variable selection in high-dimensional linear regression. MC+ combines a minimax concave penalty (MCP) with a penalized linear unbiased selection (PLUS) algorithm. The MCP provides convexity in sparse regions, while the PLUS algorithm computes a continuous piecewise linear path of solutions. MC+ achieves high probability of correct variable selection without requiring the strong irrepresentable condition used by the LASSO. It also attains certain minimax convergence rates for regression coefficient estimation. The paper proves the selection consistency of MC+ under a sparse Riesz condition and demonstrates its superior performance in simulations compared to the LASSO and SCAD. MC+ is computationally efficient and avoids the computational difficulties of nonconvex minimization. The paper also provides a general theory of penalized least squares estimation, including the continuity of estimators, unbiased risk estimation, and noise level estimation. The results show that MC+ outperforms the LASSO in variable selection accuracy and computational efficiency.