Relativistic electron beams driven by laser wakefield acceleration were utilized to produce ultrashort neutron sources. The experiment was carried out on the 38 fs, ~0.5 J, 800 nm Ti:Sapphire laser in the 10 TW UT³ laser lab at University of Texas at Austin. The target gas was a high density pulsed gas jet composed of 90% He and 10% N₂. The laser pulse with a peak intensity of 1.5×10¹⁸ W/cm² interacted with the target to create a cylindrical plasma channel of 60 mm radius (FWHM) and 1.5 mm length (FWHM). Electron beams of ~80 pC with the Gaussian energy distribution centered at 37 MeV and a width of 30 MeV (FWHM) were produced via laser wakefield acceleration. Neutron fluences of ~2.4×10⁶ per shot with hundreds of ps temporal length were generated through bremsstrahlung and subsequent photoneutron reactions in a 26.6 mm thick tungsten converter. Results were compared with those of simulations using EPOCH and GEANT4, showing agreement in electron spectrum, neutron fluence, neutron angular distribution and conversion rate.