This study aims to identify the extent to which the staff believes the factors influencing problem-solving competencies among school administrators and to relate these beliefs to the perceived problem-solving competence of the administrators based on the perceptions among staff. This study designed a survey method that involved 731 teachers and administrators from various schools in the Central and Highlands areas, Ho Chi Minh City and the Southeast and Southwest Regions in Vietnam to accomplish these purposes. Structural equation modeling in the data analysis yields a robust model fit advocated by the socio-psychological theory of belief-behavior linkage. The conclusion is that the internal environment and the efforts made to develop science, technology and international collaborations have a significantly positive relationship in explaining the problem-solving competency of school administrators. However, the existing state of the external environment severely affects the problem-solving ability of school administrators. Improvements must be made to the facilities and equipment of the schools, the working conditions and the financial resources. Theoretical implications include environment-person fit, resource-based advantage, and development psychology which broaden the understanding of problem-solving abilities. School administrators should have a practical framework emphasizing the internal and external environments and procedural and investment-focused qualities.