Delta-V assisted periodic orbits (DVAPOs) are introduced as a new type of periodic orbit around small bodies subject to strong solar radiation pressure. DVAPOs are made periodic by introducing a small deterministic delta-V within each period. This type of orbit has a simpler shape and provides higher flexibility than other periodic orbits and therefore enables missions with higher scientific value. The general theory of DVAPOs is described, including the orbit design methodology, solution-space analysis, and stability analysis. This paper clarifies that DVAPOs are a useful and feasible option for smallbody missions and exhibit unique dynamic characteristics.