The interest in layered materials is largely based on the expectation that they will be beneficial for a variety of applications, from low-power-consuming, wearable electronics to energy harvesting. However, the properties of layered materials are highly dependent on thickness, and the difficulty of controlling thickness over a large area has been a bottleneck for commercial applications. Here, we report layer-by-layer growth of SnSe2, a layered semiconducting material, via van der Waals epitaxy. The films were fabricated on insulating mica substrates with substrate temperatures in the range of 210 degrees C-370 degrees C. The surface consists of a mixture of Nand (N +/- 1) layers, showing that the thickness of the film can be defined with monolayer accuracy (+/- 0.6 nm). High-resolution transmission electron microscopy reveals a polycrystalline film with a grain size of similar to 100 nm and clear Moire patterns from overlapped grains with similar thickness. We also report field effect mobility values of 3.7 cm(2) V-1 s(-1) and 6.7 cm(2) V-1 s(-1) for 11 and 22 nm thick SnSe2, respectively. SnSe2 films with customizable thickness can provide valuable platforms for industry and academic researchers to fully exploit the potential of layered materials.