A random simplex method is proposed which could be used to evaluate the values of components in equivalent electrical circuit from impedance data. It is a combination of the Monte Carlo method and the simplex method. The first estimates are arbitrarily assigned to each component, and their final solutions could be obtained through consecutive optimizations and approximations. As a result, it is possible to find out simultaneously several unknown parameters and thus the error accumulations in the last-determined components with deconvolution can be avoided. It is especially suitable for processing impedance data when dispersion phenomenon appears. The effect of errors in impedance values on fitting results is examined by using computer-generated impedance data contaminated deliberately by a random error. The processing is demonstrated with impedance spectra measured experimentally. The advantages of the proposed random simplex method comparing with the deconvolution method, and the significance of objective function, which is the criterion of fitting, are discussed.