For studying the character of Hermite-sine-Gaussian (HSiG) beam in non-paraxial case, based on the theory of the second intensity moment and a series of complex calculations, the results of the far-filed divergence angle, waist width and M2 factor of non-paraxial Hermite-sine-Gaussian beams are derived, and the relationship of them versus the acentric parameters are studied by calculation and plot. The result indicates that the relationship of non-paraxial HSiG beam characters versus the acentric parameter is different from paraxial case. As the parameter w0/λ decrease, α→0, the far-filed divergence angle with even and odd orders approach 73.898° and 63.435°, respectively. With increasing the parameter, the waist width and M2 factor show large changes. Because of the effect of parameters, non-paraxial M2 factor can be less than 1 as well as approaching 0, which is different from paraxial case.