Modern integrated naval mission systems (NMS) built on data-distribution service (DDS) have special characteristics in development, structure, and application which, in combination, make their testing challenging. Model-based testing (MBT) is considered a promising technique for testing such systems. However, for NMS-like systems under test, due to their high complexity and cooperative ways of development, traditional MBT techniques requiring a complete model of the system internals are difficult to be used. This paper presents a scenario-based MBT approach for NMS-like systems. The approach builds scenario models to express the interaction scenarios in a DDS-based system from the external perspective. A scenario model uses an extended form of regular expression to model interaction sequences and uses basic data element restrictions (e.g., ranges and enumerations), constraints, and calculation functions to model interaction data. It can express the interaction processes in an abstract, convenient, and relatively comprehensive way. On the models, algorithms are proposed to generate directly executable test cases for testing. Experiments on a real NMS show that the approach can be used to test 21 kinds of common risky scenarios identified from historical failures reported during the development of a family of NMS. This indicates that the approach might be helpful for testing NMS-like DDS-based industrial systems.