Porous structures widely exist in nature and artifacts, which can be exploited to reduce structural weight and material usage or improve damage tolerance and energy absorption. In this study, we develop an approach to design optimised porous structures with Triply Periodic Minimal Surfaces (TPMSs) in the framework of isogeometric analysis (IGA)-based topological optimisation. In the developed method, the designed porous structures can achieve the optimal mechanical performance by controlling the density distribution under a fixed weight constraint. Firstly, the implicit functions of the TPMSs are adopted to design several types of porous elements with different densities. Secondly, an equivalent method is proposed to calculate the equivalent elastic modulus of porous elements on the basis of Energy Conservation Law. Subsequently, the functional relationships of different porous elements between the equivalent elastic modulus and the relative density are constructed. Thirdly, given the design domain represented by a trivariate B-spline solid, boundary conditions and the type of porous material, we can obtain an optimal density distribution from the IGA-based porous topological optimisation to minimise the compliance. Finally, an optimum porous structure is generated in the B-spline solid with TPMS on the basis of the optimised density distribution. Experimental results demonstrate the effectiveness and efficiency of the proposed method.