Typical model of agent computing is BDI (belief, desire and intention), in which the belief is an important attribute. In this paper, the belief is extended into knowledge belief and achieving belief. Knowledge belief stands for the knowledge an agent has, which has the characteristics of knowledge evolving and inheriting. Achievement belief stands for an event which is not achieved now but will be achieved in future. It is the personality or goal which is awared by agent. Describing these two kinds of belives by the modal logic formalizing tools in non-standard world, the reachable relationship in possible world can be described as the different phases of cognition and of belief realization. This avoids the logical omniscience problem and the logical side effect problem. Knowledge belief satisfies the KDT4 axioms, and achievement belief satisfies KD axioms. These two kind of believes can be used in mental state and mental model describing.