We demonstrated that the dumping of Josephson junctions, one of characteristic parameters of actual Josephson junctions, could be varied by quasi-particle injections by performing injection experiments using multi-terminal Josephson junction devices fabricated by using electron beam lithography. Current-voltage (I-V) characteristics of a Josephson junction exhibited a transition from hysteretic to non-hysteretic behavior with increasing injection current of a control junction placed near the Josephson junction. Mc-Cumber Stewart parameter of the junction was varied about two orders of magnitude by injection. This can be used for tunable energy dissipation in Josepshon junction devices.