The design and manipulation of magnetism in low-dimensional systems are desirable for the development of spin electronic devices. Here, we design two kinds of Co-adsorbed monolayer WS2 frameworks, i.e. Co1/WS2 and Co2/WS2, and comprehensively explore the dependences of their magnetic properties on injected charge by using first-principles calculations. The value of magnetic moment can be tuned almost linearly through injecting charge due to the modulated interaction and charge transferring between Co atom and monolayer WS2. A transition from ferromagnetism to non-ferromagnetism occurs in Co1/WS2 system when 1 e/unit cell charge is injected. Furthermore, the magnetic anisotropy can be manipulated by injecting charge as well. The magnetic anisotropy energy (MAE) in Co1/WS2 system sharply increases from -4.16 to 2.47 (0.99) meV when injected charge vary from 0.0 to 0.2 (-0.2) e/unit cell, meaning a transition of the magnetic easy axis from in-plane to out-of-plane direction. Similarly, in Co2/WS2 system, the magnetic easy axis also can be modified to out-of-plane direction through injecting 0.1 e/unit cell charge. It is found that the changes of Co-3d states are responsible for the tunable magnetic anisotropy. This work provides a theoretical understanding on effective manipulation of magnetism in low-dimensional system.