Despite the growing body of research on public employees’ innovativeness and creativity, there are limited studies examining the drivers of innovative behavior among public employees. Using Self-Determination Theory, this research examines the mediating effects of psychological needs (i.e., relatedness, competence, and autonomy) on the relationship between organizational climate for innovation and individuals’ innovative behavior. We address this issue in a quantitative study with 569 Taiwanese civil servants employing a time-lag design. In accordance with Self-Determination Theory, innovation climate is found to positively affect public employees’ innovative behavior by enhancing two psychological needs, competence and relatedness. While the innovative climate in the government enhances autonomy, this psychological need does not mediate the link between the innovation climate and innovative behavior. This study makes a valuable contribution to public management literature on public sector innovation.