In this paper, we present an approach to nonlinear system approximation, called the lattice trajectory piecewise linear (LTPWL) model. The approach involves determining a lattice piecewise linear (PWL) approximation to the state trajectory of a nonlinear system. It has been shown in the literature that the lattice PWL expression can represent any PWL function in any dimension. After the LTPWL approximation has been obtained, the order of each model piece is reduced using a Krylov projection technique. Compared to existing trajectory piecewise linear (TPWL) models, which are quasi-PWL in the whole region, LTPWL models are virtually linear in each subregion. Besides, the single output LTPWL model can be seen as a special kind of TPWL model, in which only one weight is 1, and the other weights are 0. In general, for multiple output LTPWL model, the weights set to be 1 for each component are different, which makes the LTPWL model more flexible in approximation of nonlinear function. The proposed strategy is applied to simulate diode circuits, and the experimental results show that the performance of the LTPWL model is better than that of the traditional TPWL model in terms of approximation accuracy and generalization ability.