Floating-gate memories based on two-dimensional van der Waal (2D vdW) heterostructures play an important role in the development of next-generation information technology. The diversity of 2D vdW materials and their heterostructures provides flexibility in the design of novel storage architectures. However, 2D InSe/h-BN/GaSe heterostructures are rarely reported in the field of tunable non-volatile memories, probably due to the quality limitation of materials and complex interfaces from stackings. Herein, a floating-gate 2D InSe/h-BN/GaSe memory with high performance and atmosphere stability is demonstrated. It exhibits both a large ON/OFF current ratio of ∼105 and a good extinction ratio of ∼103, with an estimated maximum storage capacity of 5.1 × 1012 cm-2. Moreover, the storage performance can be regulated by optimizing the thickness of the insulating h-BN layer. Different device configurations have been explored to validate the working mechanism. Furthermore, a simulation of biological synaptic behavior is achieved on the same prototype device. The enhanced non-volatile characteristics enable the exploration of the integrated 2D memory and potential multifunctionality.