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Based on the fact that most of real networks are directed and weighted, and the breeding of new connections generally affects the communication capacity of neighbor nodes, this paper proposes a strength-based instead of degree-based directed weighted scale-free network model where an adaptive weight evolution mechanism is introduced, and the newly added edges between existing nodes besides between existing nodes and the new node are involved in. Theoretical analysis shows the strength (in-strength and out-strength) distribution as well as degree (in-degree and out-degree) distribution of networks generated by our presented model follow a power law distribution, indicating the network is with scale-free characteristic, and the power-law exponent is independent of network size, but depends on the basic edge weight, the weight increment and the number of newly added edges. Numerous simulations further verify that numerical results are well consistent with the theoretical results, and the dependence of power-law exponents on the aforementioned parameters are also analyzed and discussed. In addition, the topological characteristics of the directed weighted scale-free network, such as the average clustering coefficient and the average path length, are demonstrated as well. • The model aims at the directed and weighted network, and it is based on node's strength distribution. • An adaptive evolution mechanism is introduced in generating networks. • The new edges are bred not only between the new node and existing nodes, but between existing nodes. • The model is verified by theoretical analysis and numerical simulations. • The impact of initial setting parameters on the scale-free characteristic is discussed. [ABSTRACT FROM AUTHOR]