The high-order Hermite-Gaussian (HG) mode squeezed light, as one of the important quantum sources, has significant application in quantum precision measurement and quantum imaging. The enhancement of spatial measurement precision largely depends on the squeezing level of high-order HG-mode quantum states. However, the squeezing level of high-order HG modes is primarily limited by the external pump power in the optical parametric oscillator (OPO) cavity. As is well known, the OPO with dual resonance for both squeezed light and pump light can lower external pump power. The generation of HG₁₀ mode squeezed light differs from that of HG₀₀ mode squeezed light, with an additional Gouy phase shift introduced between the HG₂₀ pump mode and HG₁₀ down-conversion mode within the OPO cavity. In this work, we conduct theoretical analysis and experimental generation of HG₁₀ mode squeezed light at lower external pump power by using a doubly-resonant OPO based on a wedged periodically poled KTiOPO4 (PPKTP) crystal. By precisely controlling both the propagation length of the optical field and temperature in the wedged PPKTP crystal, we simultaneously compensate for the Gouy phase shift between the HG₂₀ and HG₁₀ modes and the astigmatism induced by the frequency-dependent refractive index. This configuration allows for dual resonance of the HG₂₀ pump mode and the HG₁₀ squeezed mode, while operating under the condition close to optimal phase matching. Increasing the reflectivity of the input coupler of OPO cavity enhances the intra-cavity circulating power of the pump light, thereby reducing the required external pump power. Here, the bow-tie-shaped OPO cavity consists of two plane mirrors and two concave mirrors with a curvature radius of 50 mm. The wedged PPKTP is placed in the smallest beam waist of the cavity. The mode converter is employed to generate high-purity HG₂₀ pump mode with a measured purity of 98.0%. The mode-matching effciency of 93.0% is achieved between the high-purity HG₂₀ pump mode and the OPO cavity. The homodyne visibility of the HG₁₀ mode is 98.1%. We experimentally demonstrate the generation of 9.10 dB HG₁₀ mode squeezed light by using a doubly-resonant OPO with only 51 mW of HG₂₀ pump mode, and simultaneously achieve 9.20 dB of squeezing in the HG₀₀ mode with 27 mW of HG₀₀ pump mode. The inferred squeezing levels of both HG₁₀ mode and HG₀₀ mode squeezed light both reach up to 12.15 dB. The quantum technology has solved the pump power limitations in optical parametric oscillators, generating high-order HG mode states with high squeezing level and providing an effective method for enhancing spatial measurement precision.