John Desmond Bernal (1901-1970) was one of the most eminent scientists in molecular biology, and also regarded as the founding father of the Science of Science. His book The Social Function of Science laid the theoretical foundations for the discipline. In this article, we summarize four chief characteristics of his ideas in the Science of Science: the socio-historical perspective, theoretical models, qualitative and quantitative approaches, and studies of science planning and policy. China has constantly reformed its scientific and technological system based on research evidence of the Science of Science. Therefore, we analyze the impact of Bernal Science-of-Science thoughts on the development of Science of Science in China, and discuss how they might be usefully taken still further in quantitative studies of science.