Self-assembled quantum dots grown by molecular beam epitaxy have been a hotbed for various fundamental research and device applications over the past decades. Among them, InAs/GaAs quantum dots have shown great potential for applications in quantum information, quantum computing, infrared photodetection, etc. Though intensively studied, some of the optical nonlinear properties of InAs/GaAs quantum dots, specifically the associated two-photon absorption of the wetting and barrier layers, have not been investigated yet. Here we report a study of the photoluminescence of these dots by using direct two-photon excitation. The quadratic power law dependence of the photoluminescence intensity, together with the ground-state resonant peak of quantum dots appearing in the photoluminescence excitation spectrum, unambiguously confirms the occurrence of the direct two-photon absorption in the dots. A three-level rate equation model is proposed to describe the photogenerated carrier dynamics in the quantum dot-wetting layer-GaAs system. Moreover, higher-order power law dependence of photoluminescence intensity is observed on both the GaAs substrate and the wetting layer by two-photon excitation, which is accounted for by a model involving the third-harmonic generation at the sample interface. Our results open a door for understanding the optical nonlinear effects associated with this fundamentally and technologically important platform.