Compared to a single vortex beam, vortex array beams can increase the information transmission capacity. Therefore, studying the propagation properties of vortex array beams is significant for their optical communication applications. In this paper, we select the helical Ince-Gaussian (HIG_n,n) modes of order n and simulate the marine atmosphere turbulence using the power spectrum of the refractive index fluctuations in the marine atmosphere. The changes in intensity, phase, scintillation index and spot centroid wander of a one-dimensional array vortex beam in marine atmospheric turbulence have been investigated systematically by using the phase screen method. We find that (1) an increase in either the turbulence intensity or atmospheric turbulence inner scale enhances both the scintillation index and spot centroid wander standard deviation for HIG_n,n modes; (2) the scintillation index of HIG_n,n mode with odd n decreases with increasing mode order, and is higher than that of HIG_n,n mode for even n; (3) the HIG_n,n mode with order n>1 has better stability than the LG_0,1 mode; and (4) the higher the mode order, the smaller the standard deviation of spot centroid wander of HIG_n,n mode. In addition, we perform comparative study on the propagation performance of the linear array vortex beams (LAVBs) and HIG beams. Our study indicates that although LAVBs have better propagation performance than HIG beams, the unique structures of HIG beams can be applied to various application scenarios. Finally, the effects of both the ellipticity parameter and elliptic ring number on the propagation of the HIG modes are explored and analyzed. The results show that increasing either the ellipticity parameter or elliptic ring number is beneficial to improving the anti-turbulence ability of the HIG modes. These results offer significant guidance for the offshore vortex beams application.