An experimental study of laser driven electron acceleration in N 2 and N 2 -He mixed gas-jet target using laser pulses of duration ~60-70 fs is presented. Generation of relativistic electron beam with quasi-thermal spectra was observed at a threshold density of ~1.6×10 18 cm -3 in case of pure N 2 , and the threshold density was found to increase with increasing doping concentration of He.At an optimum fraction of 50% of He in N 2, generation of quasi-monoenergetic electron beams was observed at a comparatively higher threshold density of ~2×10 18 cm -3 , with an average peak energy of ~168 MeV, average energy spread of ~21%, and average total beam charge of ~220 pC. Electron acceleration could be attributed to the direct laser acceleration as well as the hybrid mechanism. Observation of an optimum fraction of He in N 2 (in turn threshold plasma density) for comparatively better quality electron beam generation could be understood in terms of the plasma density dependent variation in the dephasing rate of electrons with respect to transverse oscillating laser field. Results are also supported by the 2D PIC simulations performed using code EPOCH.