<p>In the present study, the combined impacts of self-generated and non-uniform magnetic fields on the acceleration of plasma electrons using circularly polarized laser pulses propagating in plasma are theoretically studied under a strongly relativistic regime. Analytical and mathematical formulations for analyzing laser pulse propagation through plasma medium with consideration of the self-generated and non-uniform magnetic fields have been obtained. The simulation results show that in comparison to without a non-uniform magnetic field, electron energy increases with an increasing <i>δ</i>-parameter. Additionally, it is recognized that the existence of both non-uniform as well as self-generated magnetic fields simultaneously increases electron transverse momentum, which increases energy. Furthermore, it is observed that when the plasma is only dominated via the self-generated magnetic fields consisting of azimuthal and axial magnetic fields, plasma electrons accelerate much less than when a non-uniform magnetic field is employed. It is also shown that higher laser intensity results in a rise in electron energy, depending on the optimal laser field and self-consistent magnetic field. Moreover, it is realized that the amounts of the slope parameter and the magnetic field can be adjusted to control electron energy gain.</p>