The local pseudopotential method (PS) has been implemented into real-space electronic structure calculations based on symmetric smoothed particle hydrodynamics (SSPH). As a simple example, we applied this SSPH to a simple atom such as H, He and Li. To evaluate SSPH with PS, the results are compared with those of the finite difference method (FD), the simple SSPH, and the usual atom calculation (AT). Similar results were obtained from both of FD and the simple SSPH. However, there are several differences between the results of the simple SSPH and that of AT. When we use SSPH with PS, the results can be controlled to those of AT, using appropriate parameters. We recognize that, in our previous study, the error between the simple SSPH and AT is mainly caused by the difference of the charge in the vicinity of the ion core. The discretization by the simple SSPH is not enough to describe the electronic structure, especially the Hartree term. Since the pseudopotential around the ion core is finite, this error reduces in our SSPH with PS. Our results show that SSPH with PS can be practically applied to electronic calculations, keeping high accuracy, SSPH with PS