Hypersonic low enthalpy laminar flows of double cone with 25°/55° geometry were simulated by using high-order WCNS (weighted compact nonlinear schemes), and their capabilities to accurately predict laminar shock wave/boundary layer interaction were examined. The simulations were performed through adopting the second order MUSCL, the third-order and the fifth-order WCNS as spatial discretization schemes, employing the secondorder dual time-stepping approach for time integration and using different flux functions, such as hybrid Roe-Rusnov, AUSMPW+ and Van Leer, for comparison. The effects of high-order methods on time and grid convergence, as well as the dissipation characteristics of flux functions, were analyzed. The numerical simulation results indicate that the highorder methods can obtain well-resolved results on coarse grid and eliminate the sensitivity of flux functions. However, the high-order methods need longer computational time to reach convergence. The computed results show good agreement with the experimental data, and the computational accuracy may be characterized as reasonable for most engineering purposes.