Magnetic skyrmions and their effective manipulations are promising for the design of next-generation information storage and processing devices, due to their topologically protected chiral spin textures and low energy cost. They, therefore, have attracted significant interest from the communities of condensed matter physics and materials science. Herein, based on density functional theory (DFT) calculations and micromagnetic simulations, we report the spontaneous 2 nm-diameter magnetic skyrmions in the monolayer CuCrP2Te6 originating from the synergistic effect of broken inversion symmetry and strong Dzyaloshinskii-Moriya interactions (DMIs). The creation and annihilation of magnetic skyrmions can be achieved via the ferroelectric to anti-ferroelectric (FE-to-AFE) transition, due to the variation of the magnetic parameter D2/|KJ|. Moreover, we also found that the DMIs and Heisenberg isotropic exchange can be manipulated by bi-axial strain, to effectively enhance skyrmion stability. Our findings provide feasible approaches to manipulate the skyrmions, which can be used for the design of next-generation information storage devices.