Pseudospectral Hartree-Fock(PSHF) gradient calculations with $6-31G^{**}$ basis set have been carried out to determine the structure of D-Asparagine molecule $(C_4N_2O_3H_8)$ with improved grids and with the BFGS method. The modified PSHF method, despite partial optimization of the gradient code, turned out to be still faster than the conventional ab initio method, GAUSSIAN 90 program by more than twice. The optimum geometry of D-Asparagine obtained by the PSHF method is in good agreement with those calculated by the GAUSSIAN 90 program (within 0.0036 ${AA}$ for bond lengths, 0.8 degrees for bond angles, and 1.6 degrees for torsional angles) except for three torsional angles. Here, rather large discrepancy of these three torsional angles (5-6 degrees) is attributed to the small differences in the optimum bond lengths and angles between the PSHF and GAUSSIAN 90 calculations.