The quantum wave function measurement of a free electron remains challenging in quantum mechanics and is subject to disputes about ψ-ontic/epistemic interpretations of the wave function. Here, we theoretically propose a realistic spectral method for reconstructing quantum wave function of an electron pulse, free-electron spectral shearing interferometry (FESSI). We use a Wien filter to generate two time-delayed replicas of the electron wave packet and then shift one replica in energy using a light-electron modulator driven by a mid-infrared laser. As a direct demonstration, we numerically reconstruct a pulsed electron wave function with a kinetic energy of 10 keV. FESSI is experimentally feasible and enables us to fully determine distinct orders of spectral phases and their physical implications in quantum foundations and quantum technologies, providing a universal approach to characterize ultrashort electron pulses.