Visual and central attention are limited in capacity. In conjunction search, visual attention is required to select the items and to bind their features (e.g., color, form, size), which results in a serial search process. In dual-tasks, central attention is required for response selection, but because central attention is limited in capacity, response selection can only be carried out for one task at a time. Here, we investigated whether visual and central attention rely on a common or on distinct capacity limitations. In two dual-task experiments, participants completed an auditory two-choice discrimination Task 1 and a conjunction search Task 2 that were presented with an experimentally modulated temporal interval between them (stimulus onset asynchrony [SOA]). In Experiment 1, Task 2 was a triple conjunction search task. Each item consisted of a conjunction of three features, so that target and distractors shared two features. In Experiment 2, Task 2 was a plus conjunction search task, in which target and distractors shared the same four features. The hypotheses for conjunction search time were derived from the locus-of-slack method. While plus conjunction search was performed after response selection in Task 1, a small part of triple conjunction search was still performed in parallel to response selection in Task 1. However, the between-experiment comparison was not significant, indicating that both search tasks may require central attention. Taken together, the present study provides evidence that visual and central attention share a common capacity limitation when conjunction search relies strongly on serial item selection.