Mental simulations are often focused on a goal in the future or a problem to be solved. Recent neuroimaging studies have associated mental simulations of the future with default network activity, but the simulations in these studies were not typically directed toward achieving a particular goal. Goal-directed simulation requires cognitive control to maintain information, make decisions, and coordinate abstract action sequences. Therefore, it should recruit not only the default network, but also executive regions. To investigate whether default network and executive regions can be coactive in the context of goal-directed simulation, we designed a problem-solving task in which participants simulated solving several specific problems in imaginary scenarios while in the MRI scanner. We analyzed brain activity during simulation relative to a semantic elaboration task and found that goal-directed simulation engaged core regions of the default network and executive dorsolateral prefrontal cortex. A functional connectivity analysis with posterior cingulate and dorsolateral prefrontal cortex seeds revealed that activity in these regions was coupled throughout the goal-directed simulation period and associated with a distributed network of other default and executive regions, including medial prefrontal cortex, medial temporal, and parietal regions.