Goal-directed behavior is a deeply important part of human psychology. People constantly set goals for themselves and pursue them in many domains of life. In this paper, we develop computational models that characterize how humans pursue goals in a complex dynamic environment and test how well they describe human behavior in an experiment. Our models are motivated by the principle of resource rationality and draw upon psychological insights about people’s limited attention and planning capacities. We find that human goal pursuit is qualitatively different and substantially less efficient than optimal goal pursuit in our simulated environment. Models of goal pursuit based on the principle of resource rationality capture human behavior better than both a model of optimal goal pursuit and heuristics that are not resource-rational. We conclude that the way humans pursue goals is shaped by the need to achieve goals effectively as well as cognitive costs and constraints on planning and attention. Our findings are an important step toward understanding humans' goal pursuit as cognitive limitations play a crucial role in shaping people’s goal-directed behavior.