Online platforms have emerged to facilitate patent transfer between academia and industry, but a recommendation method that matches patents with company needs is missing in the literature. Previous patent recommendation methods were designed mainly for query-driven patent search contexts, where user needs are given. However, company needs are implicit in the patent transfer context. The problem of profiling the needs and recommending patents accordingly remains unsolved. This research proposes a knowledge graph approach to address the problem. The proposed approach defines and constructs a patent knowledge graph to capture the semantic information between keywords in the patent domain. Then, it profiles patents and companies as weighted graphs based on the patent knowledge graph. Finally, it generates recommendations by comparing the weighted graphs based on the graph edit distance measure. During the recommendation process, three recommendation strategies (i.e., supplementary, complementary, and hybrid recommendation strategies) are proposed to profile different company needs and make recommendations accordingly. The proposed approach has been implemented and tested on a knowledge transfer platform in Jiangxi province, R.P. China. A pretest experiment shows that the proposed approach outperforms several baseline methods in terms of precision, recall, F-score, and mean average precision. User feedback from an online experiment further demonstrates the usability and the effectiveness of the proposed approach for recommending patents to companies.