Unlike graphene, the existence of bandgaps in transition metal dichalcogenides such as MoSe2 offers an attractive possibility of using single layer MoSe2 field-effect transistors (FETs) in low-power switching devices and photodetectors. Yet, the fabrication demands and the physics of MoSe2, among other reasons, suggest that multilayer MoSe2 may be more attractive than single layer MoSe2 for FET applications in a thin-film transistor configuration. In this presentation, we explore the optoelectronic properties of bottom-gate multilayer MoSe2 phototransistors fabricated on SiO2/Si substrates with mechanically exfoliated flakes. Our MoSe2 phototransistors exhibit decent field-effect mobilities (> 50 cm2 V-1 s-1) and high on/off-current ratio (> 106). For 650 nm incident laser, the device shows high photoresponsivity (> 500 A W-1) , high detectivity (> 1011 jones) and a fast response time (< 2 ms) at room temperature. These optoelectronic properties are better than those of MoSe2 phototransistors reported in literature. These results demonstrate a compelling case of multilayer MoSe2 phototransistors for applications in photodetectors.