In this paper, we propose a novel approach which selects and estimates sensitive parameters of a nonlinear model using L1-regularization. A biomechanical model have many parameters to be estimated for accurate human body simulation. However, when we have insufficient data for estimation, it occurs the overfitting problem. Therefore, we reformulate the parameter update process of the Levenberg-Marquardt (LM) optimization in order to apply the least absolute shrinkage and selection operator (LASSO) to a nonlinear least squares problem. To show the effectiveness of our method, we compare our method with other methods from application of head-neck position tracking task. As a result, our method selects sensitive parameters with much shorter computation time than other method. In addition, our method maintains goodness of fit measured by Variance accounted for (VAF) at 82.45% although reducing the number of estimated parameters.