A model of genome evolution is proposed. Based on three assumptions the evolutionary theory of a genome is formulated. The general law on the direction of genome evolution is given. Both the deterministic classical equation and the stochastic quantum equation are proposed. It is proved that the classical equation can be put in a form of the least action principle and the latter can be used for obtaining the quantum generalization of the evolutionary law. The wave equation and uncertainty relation for the quantum evolution are deduced logically. It is shown that the classical trajectory is a limiting case of the general quantum evolution depicted in the coarse-grained time. The observed smooth/sudden evolution is interpreted by the alternating occurrence of the classical and quantum phases. The speciation event is explained by the quantum transition in quantum phase. Fundamental constants of time dimension, the quantization constant and the evolutionary inertia, are introduced for characterizing the genome evolution. The size of minimum genome is deduced from the quantum uncertainty lower bound. The present work shows the quantum law may be more general than thought, since it plays key roles not only in atomic physics, but also in genome evolution.
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