L0-constrained optimization problem has been widely applied to sparse signal reconstruction (e.g., basis pursuit denoising and compressed sensing) in signal processing, statistics, and related fields. However, it is an NP-hard problem to obtain the optimal solution of the L0-constrained optimization problem in the recovery of compressive sensed signals. In this paper, we apply neurodynamic approach to solve the L0-constrained optimization problem. Based on an inverted Gaussian function, a function of L0 approximation can be obtained and a three-layer projection-type neurodynamic model is further constructed. The L0 approximation constraint condition and a convexity objective function under which the neurodynamic optimization method is guaranteed to achieve the locally convergent optimal solution. Experimental results illustrate the effectiveness of the proposed neurodynamic approach.