There is conflicting evidence regarding whether humans can make spatially optimal eye movements during visual search. Some studies have shown that humans can optimally integrate information across fixations and determine the next fixation location, however, these models have generally ignored the control of fixation duration and memory limitation, and the model results do not agree well with the details of human eye movement metrics. Here, we measured the temporal course of the human visibility map and performed a visual search experiment. We further built a continuous-time eye movement model that considers saccadic inaccuracy, saccadic bias, and memory constraints. We show that this model agrees better with the spatial and temporal properties of human eye movements and predict that humans have a memory capacity of around eight previous fixations. The model results reveal that humans employ a suboptimal eye movement strategy to find a target, which may minimize costs while still achieving sufficiently high search performance.