We investigate ground state properties of the half-filled staggered-flux Hubbard model on a square lattice. Energy gaps to charge and spin excitations and magnetic as well as dimer orders are calculated as a function of interaction strength $U/t$ by means of constrained-path quantum Monte Carlo method. It is found that the system is a semi-metal at $U/t\lesssim 5.6$ and a Mott insulator with long-range antiferromagnetic order at $U/t \gtrsim 6.6$. In the range $5.6\lesssim U/t\lesssim 6.6$, the ground state is an correlated insulator where both magnetic and dimer orders are absent. Furthermore, spin excitation in the intermediate phase appears to be gapless, and the measured spin-spin correlation function exhibits power-law decaying behavior. The data suggest that the non-magnetic ground state is a possible candidate for the putative algebraic spin liquid.