We present analytical results of the equation of state (EOS) described by a model of thermal quark mass and magnetic potential term introduced in Polyakov–Nambu–Jona–Lasinio (PNJL) model for two-flavour quarks. Under the influence of thermal quark mass and magnetic field term in the potential, the calculated results of EOS using the model are enhanced in a good pattern up to the temperature $T=2.2T_c$ MeV and can follow result similar to the unmagnetised field when the temperature is increased beyond $T=2.2T_c$ MeV. The result shows that the thermodynamic behaviour agrees well with the standard properties of quantum chromodynamics (QCD) thermodynamics and enhance the result up to 2.2$T_c$ from the earlier predicted results and show the same behaviour beyond 2.2$T_c$ MeV.