In recent years, more and more researchers have paid attention to the hyperentanglement, because it plays a very important role in the quantum information and quantum communication. Continuous-variable hyperentangled state with orbital angular momentum and spin angular momentum has a promising application in the parallel processing of continuous-variable multi-channel quantum information and multiparameters quantum metrology. Recently Liu et al. (2014 Phys. Rev. Lett.113 170501) have produced a quantum correlation of about 1.00 dB for the continuous-variable hyperentangled state by a type-II non-degenerate optical parametric amplifier. The generation of continuous-variable hyperentangled state is affected by the mode matching between the pump field and the down-conversion field, since the hyperentanglement contains spatial high-order transverse mode entanglement. In the present paper, we first theoretically analyze the relationship between the pump and the two down-conversion modes and demonstrate the dependence of the inseparability on normalized pump power for the different pump modes. Hence, we find that the optimal pump mode is the superposition of ${\rm{LG}}_0^0$ mode and ${\rm{LG}}_1^0$ mode. However, the optimal pump mode is rather complicated and difficult to experimentally generate, in the alternative scheme the ${\rm{LG}}_1^0$ mode is used as the pump field to obtain the optimal entanglement. In the experiment, the ${\rm{LG}}_1^0$ mode is produced by converting the HG₁₁ mode with a π/2 converter, and here the HG₁₁ mode is achieved by tailoring the fundamental mode with a four-quadrant phase mask and a filtering cavity. Then the ${\rm{LG}}_0^0$ mode or ${\rm{LG}}_1^0$ mode is used as the pump field to drive the non-degenerate optical parametric amplifier operating in spatial multimode. When the non-degenerate optical parametric amplifier is operated in the de-amplification, the hyperentanglement with orbital angular momentum and spin angular momentum is produced. The output entangled b