The expression for the scintillation index of radial Gaussian array beams propagation in non-Kolmogorov turbulence was derived by using the extended Huygens-Fresnel principle and Rytov method. The influences of the ring radius r0, beam number N, general exponent α and propagation distance L on the on-axis and off-axis scintillation index were studied. The results show that both the on-axis and off-axis scintillation index rise initially as α becomes larger, but later the scintillation reduce as α grows further. It is worth noting that beams with different r0 reach its maximum scintillation correspond to different α. The scintillation index values of array beams are smaller than that of a Gaussian beam around the on-axis point, but with the increase of the transverse coordinate px the scintillation index values become larger than that of a Gaussian beam. Scintillation index decreases with the increase of N, but the dependence of scintillation on r0 is not monotonic.