In a sweep cover problem, points of interest (PoIs) are required to be visited by mobile sensors periodically. The time span between two consecutive visits of a PoI is the sweep-period of that PoI. In this paper, we study the min sweep-period sweep cover problem with a distance constraint (MinSPSC[Formula: see text]). Given [Formula: see text] mobile sensors with speed [Formula: see text], [Formula: see text] base stations and a distance constraint [Formula: see text], the goal of MinSPSC[Formula: see text] is to design routes for the mobile sensors such that the maximum sweep-period is minimized under the condition that every mobile sensor has to visit a base station before traveling distance [Formula: see text]. We present an [Formula: see text]-approximation algorithm for MinSPSC[Formula: see text], where [Formula: see text] is the maximum distance between a PoI and a base station.