Constrained least-square design of two-dimensional quadrantally symmetric linear-phase FIR filters is formulated as minimizing the total squared approximation error subject to specified passband and stopband ripples.A projected least-square algorithm that alternatively updates the active set of constraint and projects the unconstrained minimal point successively onto the boundary of the active constraints is presented.Applications in the design of circular and diamond-shaped low-pass FIR filters demonstrate that the algorithm is much more efficient than an active-set based algorithm and an interior-point based algorithm.