Abstract Determining the charged particle trajectories in the inhomogeneous electric and magnetic fields is the common problem in the plasma physics. For the tokamak plasma, the orbits of the captured fast ions are affected both by the curvature and gradient of the magnetic field. In the present work, the fast ion trajectories and their guiding-centre orbits in a mega ampere spherical tokamak reactor are found with employing the numerical code, that was elaborated by our team, together with the leap-frog and Runge-Kutta techniques. The magnetic field is calculated by solving the Grad-Shafranov equation at the fixed boundaries on the non-homogeneous mesh grid. The obtained results show that the ions with the energies in the range 20 keV - 80 keV can describe the typical banana orbits as well as the passing trajectories in the poloidal plane. Finally, the numerical simulation scheme stability is tested.