Uncrewed aerial vehicle (UAV)-assisted joint communication and localization (JCAL) system have great potential and capacity to make future Internet of Things efficient, safe, smart, reliable, and sustainable. Generally, the traditional UAV path planning methods set the flying duration and hovering duration of UAVs as constants, and ignore the importance of UAV operation time in emergency rescue and other scenarios. In this article, we consider the path planning and time scheduling problem of UAV-assisted JCAL system for minimizing the UAV operation time under the constraints of the localization accuracy, communication message, and energy loss. Specifically, we first formulate path planning and time scheduling problem for UAV-assisted JCAL system and derive Cram & eacute;r-Rao bound (CRB) as the localization accuracy constraint. The variables in the constraints of localization accuracy, communication overhead, and energy loss are deeply coupled, which leads to nonconvex optimization problems. Next, to solve the high nonconvex problem, we divide the original problem into two subproblems, i.e., time scheduling subproblem and path planning subproblem. We use equivalent convex transformation and successive convex approximation (SCA) to transform the nonconvex constraints into convex forms for solving the subproblems, respectively. Lastly, aiming to the robust problem of target and channel parameters, we convert the robust constraints into convex constraint forms by equivalent proof and S-Procedure. On this basis, we develop a robust algorithm for solving the uncertainty of target and channel parameters. Simulation results verify the feasibility of the proposed methods.