The study for the time-varying of Betas is one of the hot topics in modern capital pricing theory, the literatures from domestic and abroad have been limited to empirical tests and improvement in estimation methods．But in this Paper, we applied classical CAPM theory, together with differential equation knowledge to investigate and research the determinants of the inter-temporal Betas as well as the relation between the Betas，even deduced the theoretica1 structure of time—varying Betas, furtherly, attained the numerical solution of the Betas resorting to the optimal method．What’s more is that we gave an empirical example from a company to show the dynamic efficient frontier and the trace of the Beta each period. All of these perfect and develop the modern capital pricing theory, also improve the explanatory power of the Beta for the real phenomena of finance markets．

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