We propose a new modification of Bellman's quasilinearization method such that at any iteration step, it works with an approximate solution of the original nonlinear system and with new approximation of parametersα(k+1)which are close enough to the previous ones. As an output, this approach provides a construction of a convergent sequence of parameters where the limit is the best approximation of parameters of a given system. We apply this method to a mathematical model describing BSP-kinetics in the human liver.