The first V R _ { c } I _ { c } bands light curves of MQ UMa are presented and analyzed using the Wilson-Devinney ( W-D ) program . It is discovered that MQ UMa is an A-subtype contact binary with a high fill-out ( f= 82 \% ) and a low mass ratio ( q = 0.195 ) , which indicates that it is in the late evolutionary stage of late-type tidal-locked binary stars . The mass of the primary and secondary stars are estimated and the evolutionary status of the two components are placed in the H-R diagram . The W-D solutions also indicates that MQ UMa may be a triple system with an F5V type additional component . A sample of sixteen high fill-out , low mass ratio overcontact binaries are collected and their possible evolution scenarios are discussed . Using the five times of light minimum recently observed together with those collected from literatures , the authors find that the observed-calculate ( O - C ) curve exhibits a cyclic period variation . The cyclic period change also reveals the presence of a tertiary component , which may play an important role in the formation and evolution of this binary system by drawing angular momentum from the central system .