We present the temperature-dependent susceptibility and specific heat measurement of spinel ZnV2O4. The structural transition with orbital ordering and the antiferromagnetic transition with spin ordering were observed at 50 K and 37 K, respectively. By analysis of the hysteresis behavior between the specific heat curves obtained in warming and cooling processes, the structural transition was confirmed to be the first-order transition, while the antiferromagnetic transition was found to be of the second-order type. At the structural transition, the latent heat and entropy change were calculated from the excess specific heat, and the derivative of pressure with respect to temperature was obtained using the Clausius-Clapayron equation. At the magnetic transition, the width of the critical fluctuation region was obtained to be about 0.5 K by comparing with Gaussian fluctuations. In the critical region, the critical behavior was analyzed by using renormalization-group theory. The critical amplitude ratio A+ /A-=1.46, which deviates from the 3D Heisenburg model; while the critical exponent α is -0.011, which is close to the 3D XY model. We proposed that these abnormal critical behaviors can be attributed to strong spin-orbital coupling accompanied with the antiferromagnetic transition. Moreover, in the low temperature range (2-5 K), the Fermi energy, the density of states near the Fermi surface, and the low limit of Debye temperature were estimated to be 2.42 eV, 2.48 eV-1, and 240 K, respectively.