The Chebyshev design of complex finite impulse response (FIR) filters with frequency equality-and-inequality constraints is considered in this paper. Firstly, a sufficient condition for the optimal solution to such design problems is established. According to the condition, we then extend the algorithm proposed in  from the inequality constrained only to the equality-and-inequality constrained case by taking the weights at equality constrained points to be infinity or a sufficiently great number. The generalized approach is guaranteed to converge fast to the optimal solution provided the optimal solution exists. Finally, some examples are presented to illustrate the performance of the approach.