Growing role of intellectual capital within organizations is affecting new strategies related to knowledge management and competence development. Among different aspects related to this field, knowledge diffusion has become one of interesting areas from both practitioner and researchers perspective. Several models were proposed with main goal to simulate diffusion and to explain the nature of these processes. Existing models are focused on knowledge diffusion and they assume diffusion within a single layer using knowledge representation. From the organizational perspective connecting several types of knowledge and modelling changes of competence can bring additional value. In the article we extended existing approaches by using multilayer diffusion model and focused on analysis of competence development process. The proposed model describes competence development process in a new way through horizontal and vertical knowledge diffusion in multilayer network. In the network, agents collaborate and interchange various kind of knowledge through different layers and this mutual activities affect the competences in a positive or negative way. Taking under consideration workers cognitive and social abilities and the previous level of competence the new competence level can be estimated. The model is developed to support competence management in different organizations.