Negative magnetoresistance (NMR) is a marked feature of Dirac semimetals, and may be caused by multiple mechanisms, such as the chiral anomaly, the Zeeman energy, the quantum interference effect, and the orbital moment. Recently, an experiment on Dirac semimetal Cd3As2 thin films revealed a new NMR feature that depends strongly on the thickness of the sample [T. Schumann et al., Phys. Rev. B 95, 241113(R) (2017)]. Here, we introduce a mechanism of inducing NMR via the presence of the Van Hove singularity (VHS) in the density of states. A theoretical fitting of the experimental data on magnetoc...