In this paper proposed a method of predicting the impedance below the borehole in front of the bit using output seismic trace by corridor stack on upgoing wavefronts of zero-offset VSP data. The method of nonlinear iterative inversion using the preconditioned conjugate gradient method and modifying the damping factor in order to sure the stability and convergence of the inversion results is carried out. The preconditioned CG method with decreasing condition number of the Hessian matrix, improves the convergence rate. Levenberg-Marquardt method, calculates the damping factor automatically in each iteration. Theoretical models and actual data show the effectiveness of this method for pre-drilling prediction using VSP data.