Abstract: Adaptive subgradient projection method(ASPM) is proposed in this paper for sparse reconstruction in compressed sensing(CS). Stochastic property convex set which contains the sparse reconstruction signal is established by the CS reconstruction model firstly. Then parallel subgradient projection is adopted to convert projection onto convex sets to projection into multiple closed halfspaces. Finally, the updated sparse reconstruction signal vector is projected onto the constrained set. Meanwhile, mechanism which adaptively adjusts inflation parameter in different iterations has been designed for fast convergence. Theoretical analysis and simulation results conclude that this algorithm has fast convergence, lower reconstruction error, and exhibits higher robustness in different noise intensity.