Wikipedia has become a high coverage knowledge source which has been used in many research areas such as natural language processing, text mining and information retrieval. Several methods have been introduced for extracting explicit or implicit relations from Wikipedia to represent semantics of concepts/words. However, the main challenge in semantic representation is how to incorporate different types of semantic relations to capture more semantic evidences of the associations of concepts. In this article, we propose a semantic concept model that incorporates different types of semantic features extracting from Wikipedia. For each concept that corresponds to an article, four semantic features are introduced: template links, categories, salient concepts and topics. The proposed model is based on the probability distributions that are defined for these semantic features of a Wikipedia concept. The template links and categories are the document-level features which are directly extracted from the structured information included in the article. On the other hand, the salient concepts and topics are corpus-level features which are extracted to capture implicit relations among concepts. For the salient concepts feature, the distributional-based method is utilised on the hypertext corpus to extract this feature for each Wikipedia concept. Then, the probability product kernel is used to improve the weight of each concept in this feature. For the topic feature, the Labelled latent Dirichlet allocation is adapted on the supervised multi-label of Wikipedia to train the probabilistic model of this feature. Finally, we used the linear interpolation for incorporating these semantic features into the probabilistic model to estimate the semantic relation probability of the specific concept over Wikipedia articles. The proposed model is evaluated on 12 benchmark datasets in three natural language processing tasks: measuring the semantic relatedness of concepts/words in general and in the biomedical domain, semantic textual relatedness measurement and measuring the semantic compositionality of noun compounds. The model is also compared with five methods that depends on separate semantic features in Wikipedia. Experimental results show that the proposed model achieves promising results in three tasks and outperforms the baseline methods in most of the evaluation datasets. This implies that incorporation of explicit and implicit semantic features is useful for representing semantics of concepts in Wikipedia.