Our previous research [J. X. Gong et al. Phys. Plasmas 24, 033103 (2017)] shows that in the presence of an external longitudinal magnetic field, there is no cut-off density when a right-handed (RH-) circularly polarized (CP) laser propagates in the plasmas. In this work, the proton acceleration driven by an RH-CP laser interaction with a pre-magnetized cone target filled with a pre-formed plasma is investigated under the mechanism of target normal sheath acceleration. The strength of the external magnetic field considered in this paper is comparable to that of the incident laser. The two-dimensional particle-in-cell simulation results show that with an external longitudinal magnetic field, both the energy and yield of protons accelerated by the sheath electric field at the rear of the target are remarkably increased because of the higher coupling efficiency from RH-CP laser energy to electrons and the more efficient electron acceleration. Electrons can be converged remarkably by the external magnetic field and the divergence of protons can be controlled evidently by the collimated electrons. The maximum cut-off energy of protons with an imposed longitudinal magnetic field can be promoted to be as high as 82 MeV. Detailed simulation results show that the maximum energy of protons increases with the increasing initial external magnetic field.