Visual search is an important skill in navigating and locating objects (a target) among distractors in our environment. Efficient and faster target detection involves reciprocal interaction between a viewer's attentional resources as well as salient target characteristics. The neural correlates of visual search have been extensively investigated over the last decades, suggesting the involvement of a frontal-parietal network comprising the frontal eye fields (FEFs) and intraparietal sulcus (IPS). In addition, activity and connectivity of these network changes as the visual search become complex and more demanding. The current functional magnetic resonance imaging study examined the modulation of the frontal-parietal network in response to cognitive demand in 22 healthy adult participants. In addition to brain activity, changes in functional connectivity and effective connectivity in this network were examined in response to easy and difficult visual search. Results revealed significantly increased activation in FEF, IPS, and supplementary motor area, more so in difficult search than in easy search. Functional and effective connectivity analyses showed enhanced connectivity in the frontal-parietal network during difficult search and enhanced information transfer from left to right hemisphere during the difficult search process. Our overall findings suggest that cognitive demand significantly increases brain resources across all three measures of brain processing. In sum, we found that goal-directed visual search engages a network of frontal-parietal areas that are modulated in relation to cognitive demand.