||This study investigated the variation of the osculating orbit elements of a spacecraft propelled by photonic laser propulsion (PLP) under the two-body problem assumption. The PLP thrusting system can produce continuous and constant thrust. This paper first reviewed its basics and then studied its influences on the variation of osculating orbit elements given a small PLP thrust. Gauss’s equations, perturbation theory, and normalization were introduced to investigate this problem. Our work approached the problem by studying the influences of small planar and out-of-plane PLP thrusts, respectively. Bounds on the variation of orbit elements were derived, and a sufficient condition that traps the mission spacecraft in the vicinity of the mother ship was also found. Numerical simulations are also presented to verify our results, including the bounds and the sufficient conditions. The results obtained in this paper are directly applicable to the usage of PLP thrust, a new type of thrusting system, in the future, and are potentially helpful to various space missions, especially interplanetary travel.