The performances of the power-law formalism method (PLFM) and Newton-Raphson method (NRM) are compared by applying them to a non-linear least square problem for determination of the maximum reaction rate, V-m, and Michaelis constant, K-m, in an immobilized enzyme system following Michaelis-Menten kinetics. A detailed numerical investigation indicates that 1) the accuracies of the solutions (V-m and K-m) obtained by these two methods are almost the same and very high; 2) however, the rate of convergence in PLFM is higher than that in NRM; and 3) the basin of attraction for PLFM is much wider than that of NRM. Advantages of PLFM are discussed based on the experimental data in the hydrolysis of soluble starch by glucoamylase immobilized on a porous honeycomb monolith. The result suggests that the nonlinear least-square method combined with PLFM is useful for many optimization problems in engineering fields.