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Parameter estimation of Fricke-Morse model of biological tissue is widely used in bioimpedance data processing and analysis. Complex nonlinear least squares (CNLS) data fitting is often used for parameter estimation of the model, but limitations such as high processing time, converging into local minimums, need for good initial guess of model parameters and non-convergence have been reported. Thus, there is strong motivation to develop methods which can solve these flaws. In this paper a novel real-time method for parameter estimation of Fricke-Morse model of biological cells is presented. The proposed method uses the value of characteristic frequency estimated from the measured imaginary part of bioimpedance, whereupon the Fricke-Morse model parameters are calculated using the provided analytical expressions. The proposed method is compared with CNLS in frequency ranges of 1 kHz to 10 MHz (beta-dispersion) and 10 kHz to 100 kHz, which is more suitable for low-cost microcontroller-based bioimpedance measurement systems. The obtained results are promising, and in both frequency ranges, CNLS and the proposed method have accuracies suitable for most electrical bioimpedance (EBI) applications. However, the proposed algorithm has significantly lower computation complexity, so it was 20-80 times faster than CNLS.