In this paper, the (3+1)-dimensional Jimbo-Miwa equation is solved by Fan sub-equation method with improved algorithms. As a result, many new and more general travelling wave solutions are obtained including kink-shaped soliton solutions, rational solutions, triangular periodic solutions, Jacobi and Weierstrass doubly periodic wave solutions. At a certain limit condition, the obtained Jacobi elliptic periodic wave solutions can degenerate into soliton solutions. It is shown that the improved algorithms of Fan sub-equation method can lead to such solutions with external linear functions possessing two remarkable evolutionary properties: (i) the wave propagation is skew; (ii) the amplitude enlarges along with the increasing time.