Proton energy enhancement in a combinational radiation pressure and bubble regime by applying a positively chirped laser pulse has been studied using a series of two-dimensional particle-in-cell simulations. In this regime, the proton injection in the half-first period of an excited plasma wave in an under-dense plasma plays the main role in the acceleration process. Moreover, exciting as high as large-amplitude plasma waves can significantly increase the conversion efficiency of laser energy into kinetic energy of the trapped protons. Here, the utilization of the positively chirped laser pulse is proposed as an effective approach to excite the higher amplitude wake in the combinational regime. Our studies indicate that in the positively chirped combinational regime, the plasma wake with approximately two-fold enhancement is produced that results in the generation of the proton bunch with the narrower energy spread and also the peak enhancement by a factor of two, compared with the un-chirped one. This improvement in proton energy reveals that the chirped laser pulse can be introduced as a tool to tune the energy of generated protons in the combinational radiation pressure and bubble regime.