The spin- Heisenberg model on square lattices is investigated via the finite projected entangled pair states (PEPS) method. Using the recently developed gradient optimization method combined with Monte Carlo sampling techniques, we are able to obtain the ground state energies that are competitive with the best results. The calculations show that there is no Néel order, dimer order, or plaquette order in the region of , suggesting a single spin liquid phase in the intermediate region. Furthermore, the calculated staggered spin, dimer, and plaquette correlation functions all have power law decay behaviors, which provide strong evidence that the intermediate nonmagnetic phase is a single gapless spin liquid state.