Recently, Q.-P. Ding et al. [Phys. Rev. B 95, 184404 (2017)] reported that their nuclear magnetic resonance (NMR) study on EuCo2As2 successfully characterized the antiferromagnetic (AFM) propagation vector of the incommensurate helix AFM state, showing that NMR is a unique tool for determination of the spin structures in incommensurate helical AFMs. Motivated by this work, we have carried out 153Eu, 31P, and 59Co NMR measurements on the helical antiferromagnet EuCo2P2 with an AFM ordering temperature TN=66.5 K. An incommensurate helical AFM structure was clearly confirmed by 153Eu and 31P NMR spectra on single-crystalline EuCo2P2 in zero magnetic field at 1.6 K and its external magnetic field dependence. Furthermore, based on 59Co NMR data in both the paramagnetic and incommensurate AFM states, we have determined the model-independent value of the AFM propagation vector k=(0,0,0.73±0.09)2π/c, where c is the c-axis lattice parameter. The temperature dependence of k is also discussed.