Social workers are tasked with the heavy responsibility of addressing societal problems and helping people in need, so the ability to solve a wide range of problems efficiently and effectively is essential for their daily responsibilities. Although recent studies have provided evidence for the salutary effects of psychological capital (PsyCap), including hope, efficacy, resilience and optimism, on job performance and well‐being, the mechanism through which PsyCap operates has not been empirically examined. Adopting the social problem‐solving theory, this study proposes that PsyCap is a positive psychological resource that enhances the ability to solve work problems, which provides an explanation for how PsyCap can produce work‐related benefits. Due to hopeful, efficacious, resilient and optimistic attributes, social workers who possess a high level of PsyCap are expected to engage in rational problem‐solving. Since social workers who possess a low level of PsyCap have less psychological resources to deal with job demands, they are expected to engage in impulsivity‐carelessness and avoidance strategies. A 2‐wave longitudinal study with a 3‐month interval was conducted on a sample of 400 full‐time social workers in Hong Kong. Cross‐lagged analysis showed that PsyCap at T1 increased rational problem‐solving and decreased avoidance at T2. These effects were nonreciprocal. A follow‐up qualitative study was conducted to contextualise and enrich the quantitative findings. In‐depth interviews revealed that social workers faced task‐related, interpersonal and organisational problems. They took an active or passive approach to problems depending on their level of PsyCap. Theoretical and practical implications for the social service sector are discussed.