Understanding the microscopic mechanisms for the nucleation and growth of two-dimensional molybdenum diselenide (2D MoSe2) via chemical vapor deposition (CVD) is crucial towards the precisely controlled growth of the 2D material. In this work, we employed a joint use of transmission electron microscopy and CVD, in which the 2D MoSe2 were directly grown on a graphene membrane based on grids, that enables the microstructural characterization of as-grown MoSe2 flakes. We further explore the role of hydrogen gas and find: in an argon ambient, the primary products are few-layer MoSe2 flakes, along with MoO x nanoparticles; while with the introduction of H2, single-layer MoSe2 became the dominant product during the CVD growth. Quantitative analysis of the effects of H2 flow rate on the flake sizes, and areal coverage was also given. Nevertheless, we further illuminated the evolution of shape morphology and edge structures of single-layer MoSe2, and proposed the associated growth routes during a typical CVD process.