This Letter defines thirteen useful correlation measures for directed weighted complex network analysis. First, in-strength and out-strength are defined for each node in the directed weighted network. Then, one node-based strength-strength correlation measure and four arc-based strength-strength correlation measures are defined. In addition, considering that each node is associated with in-degree, out-degree, in-strength and out-strength, four node-based strength-degree correlation measures and four arc-based strength-degree correlation measures are defined. Finally, we use these measures to analyze the world trade network and the food web. The results demonstrate the effectiveness of the proposed measures for directed weighted networks.