A sequential three-dimensional (3D) particle-in-cell simulation code PICPSI-3D with a user friendly graphical user interface (GUI) has been developed and used to study the interaction of plasma with ultrahigh intensity laser radiation. A case study of laser–plasma-based electron acceleration has been carried out to assess the performance of this code. Simulations have been performed for a Gaussian laser beam of peak intensity $5 \times 10^{19}$ W/cm² propagating through an underdense plasma of uniform density $1 \times 10^{19}$ cm^-3, and for a Gaussian laser beam of peak intensity $1.5 \times 10^{19}$ W/cm² propagating through an underdense plasma of uniform density $3.5 \times 10^{19}$ cm^-3. The electron energy spectrum has been evaluated at different time-steps during the propagation of the laser beam. When the plasma density is $1 \times 10^{19}$ cm^-3, simulations show that the electron energy spectrum forms a monoenergetic peak at $\sim 14$ MeV, with an energy spread of $\pm 7$ MeV. On the other hand, when the plasma density is $3.5 \times 10^{19}$ cm^-3, simulations show that the electron energy spectrum forms a monoenergetic peak at $\sim 23$ MeV, with an energy spread of $\pm 7.5$ MeV.