Recent discovery of intrinsic ferromagnetism in Fe3GeTe2 (FGT) monolayer [ Deng, Y.; et al. Nature 2018, 563, 94-99; Fei, Z.; et al. Nat. Mater. 2018, 17, 778-782 ] not only extended the family of two-dimensional (2D) magnetic materials but also stimulated further interest in the possibility to tune their magnetic properties without changing the chemical composition or introducing defects. By means of density functional theory computations, we explore strain effects on the magnetic properties of the FGT monolayer. We demonstrate that the ferromagnetism can be largely enhanced by the tensile strain in the FGT monolayer due to the competitive effects of direct exchange and superexchange interaction. The average magnetic moments of Fe atoms increase monotonically with an increase in biaxial strain from -5 to 5% in FGT monolayer. The intriguing variation of magnetic moments with strain in the FGT monolayer is related to the charge transfer induced by the changes in the bond lengths. Given the successful fabrication of the FGT monolayer, the strain-tunable ferromagnetism in the FGT monolayer can stimulate the experimental effort in this field. This work also suggests an effective route to control the magnetic properties of the FGT monolayer. The pronounced magnetic response toward the biaxial strain can be used to design the magnetomechanical coupling spintronics devices based on FGT.