In the present manuscript, we have investigated the effect of chirped laser pulse envelope to study electron acceleration in vacuum. For this purpose, we have chosen two different pulse shapes, i.e trapezoidal pulse envelope and Sin4 pulse envelope. Electron has been injected axially to the front of the tested envelopes. In all calculations, the front end of each pulse is presumed to have caught up with the electron at t = 0 at the coordinate origin. The relativistic Newton-Lorentz equations of motion of electron in the field of the laser pulse have been analytically and numerically solved. By optimizing laser and frequency chirp parameters, the energy gain of the order of GeV is obtained, and it has been noticed that under the similar range of phases (0 to 2π) and laser intensity parameter (a0 = 3), trapezoidal pulse envelope shows better result than Sin4 pulse envelope on effective electron acceleration in vacuum.