The monolayer WSe₂ is interesting and important for future application in nanoelectronics, spintronics and valleytronics devices, because it has the largest spin splitting and longest valley coherence time among all the known monolayer transition-metal dichalcogenides (TMDs). To obtain the large-area monolayer TMDs crystal is the first step to manufacture scalable and high-performance electronic devices. In this letter, we have successfully fabricated millimeter-sized monolayer WSe₂ single crystals with very high quality, based on our improved mechanical exfoliation method. With such superior samples, using standard high resolution angle-resolved photoemission spectroscopy, we did comprehensive electronic band structure measurements on our monolayer WSe₂. The overall band features point it to be a 1.2 eV direct band gap semiconductor. Its spin splitting of the valence band at K point is found as 460 meV, which is 30 meV less than the corresponding band splitting in its bulk counterpart. The effective hole masses of valence bands are determined as 2.344 m_e at Γ, and 0.529 m_e as well as 0.532 m_e at K for the upper and lower branch of splitting bands, respectively. And screening effect from substrate is shown to substantially impact on the electronic properties. Our results provide important insights into band structure engineering in monolayer TMDs. Our monolayer WSe₂ crystals may constitute a valuable device platform.