It is essential to mitigate power amplifier (PA) nonlinear (NL) effects to achieve energy-efficient radio communications. To restore the transmit signal quality, digital pre-distortion (DPD) is widely used. Recently, fast convergence DPD (FC-DPD) which offers good PA linearization has been proposed for next-generation broadcasting systems. However, it suffers from complexity issues and this paper addresses that drawback and we propose a low-complex version to make it hardware-friendly. We achieve significant complexity reduction by simplifying the Jacobian computation needed in the FC-DPD algorithm. This scheme can be extended to any memory-less PA model or a measured PA fitted to a polynomial model. We have provided proof that the proposed technique has linear complexity and the simulation results indicate that the proposed scheme achieves performance close to the FC-DPD algorithm. This method can be applied to other transmission systems as well.