Neural correlate of human inductive reasoning process is still unclear. Number series and letter series completion are two typical inductive reasoning tasks, and with common core component of rule induction. Previous studies have demonstrated that different strategies are adopted in number series and letter series completion tasks even the underlying rules are identical. In the present study, we examined cortical activation as a function of two different reasoning strategies for solving series completion tasks. The retrieval strategy, used in number series completion tasks, involves direct retrieving of arithmetic knowledge to get the relations between items. The procedural strategy, used in letter series completion tasks, requires counting a certain number of times to detect the relations linking two items. The two strategies require essentially the equivalent cognitive processes, but have different working memory demands (the procedural strategy incurs greater demands). The procedural strategy produced significant greater activity in areas involved in memory retrieval (dorsolateral prefrontal cortex, DLPFC) and mental representation/maintenance (posterior parietal cortex, PPC). An ACT-R model of the tasks successfully predicted behavioral performance and BOLD responses in DLPFC and PPC. The present findings support a general-purpose dual-process theory of inductive reasoning regarding the cognitive architecture.