The paper presents a scheme of vacuum electron acceleration due to tightly focused linearly polarized (LP) frequency chirped laser in the presence external magnetic field. The focused terawatt chirped laser pulse and the external axial magnetic field enable the electron of few MeV initial energy to attain high energy in GeV range, hence, explore the possibility of efficient electron acceleration. This can be achieved by optimizing the focused terawatt chirped laser and axial magnetic field parameters for resonance, which is realized between the electron and electric field of the tightly focused laser pulse. The frequency chirp plays a crucial role in enforcing resonance condition for longer duration and the applied magnetic field strongly enforces the electron to remain in the accelerating phase, thereby, both factors are equally imperative for accomplishing high electron energy gain in GeV. The presence of optimum axial magnetic field (~8.5 MG) along with optimum value of linear frequency chirp for laser intensity 1.38 × 1020 W/cm2 results in electron beam with energy ~5.78 GeV. During acceleration process, electron energy gain is highly sensitive to the initial phase of laser along with the frequency chirp and magnetic field. Electron trajectories in the influence of frequency chirp and magnetic field are also analyzed.