The invention relates to a distributed asynchronous optimization method based on continuous convex approximation and belongs to the field of network communication. The method comprises the following steps of: S1, constructing a problem model, namely selecting a global objective function of an actual problem; S2, initializing a local variable held by each node, and setting the maximum number of iterations; S3, constructing a directed strongly-connected unbalanced source network, and adding virtual nodes on the basis of the directed strongly-connected unbalanced source network to construct an augmented network; S4, setting a time delay threshold, the number of iterations and system parameters; S5, determining the relationship between an activated node and a time delay value associated with the activation node; S6, clearing out-of-date information in the system; S7, selecting an agent function, and setting proper step length and momentum parameters; and S8, enabling the activated node tocommunicate with the neighborhood or update by utilizing a time delay value variable, and enabling a non-activated node to keep the current variable value to enter the next iterative update until thethreshold value of the number of iterations is reached. The method has high robustness and fault tolerance for an asynchronous network, and the utilization efficiency of a communication link is improved.