The authors present a numerical method for the Chebyshev approximation of minimum phase FIR digital filters. This method is based on solving a least squares (LS) problem iteratively. At each iteration, the desired response is transformed so as to have an equiripple magnitude error. This method makes it possible to design minimum phase FIR filters whose magnitude error is quasi-equiripple. Using this method, a quasi-equiripple solution is obtained very quickly. Since the proposed methods do not require any time-consuming optimisation procedure, they require less computational complexity than conventional methods. Finally, some examples to illustrate the advantage of the proposed methods are shown.