The electron spins of ZnCr₂Se₄ order antiferromagnetically while the nearest neighbor exchange interaction is ferromagnetic. Therefore, exchange interaction between ions at least up to 4^th nearest neighbor should be considered, which makes the description of the spin system very complex and challenging. In this work, we measure zero field nuclear magnetic resonance (NMR) of ⁵³Cr (I=3/2) showing complex features with six peaks. Below 6 K, asymmetric anomaly in the spectra appears, similar to the previously reported NMR data of BiFeO₃. This observation is attributed to the change in T₂ relaxation mechanism of ⁵³Cr nuclei indicating unexpected state change. Complex spectra with six peaks and powder-like signal distribution are observed indicating the presence of anisotropic hyperfine interaction and nuclear quadrupole resonance. Our measurement also reconfirms the spin spiral ordering.