This paper concerns with the parameter estimation of nonlinear discrete-time systems from noisy state measurements in state-space form. A sparse Bayesian convex optimisation algorithm was proposed for the parameter estimation and prediction. The proposed method takes full account of the data correlation, parameter priori, constrains, which is explicitly modeled by Bayesian sparse learning and optimisation. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions and the number of basis function is generated randomly. The main identification challenge resides in two aspects: first, a new objective function can be obtained by Stein approximation method in the convex optimization problem. Second, a recursive least squares estimation with L1-regularization is developed, wherein the regularization parameter is selected from the point of optimization. Compared with the function maximum likelihood(ML) method only, it usually captures more information about the dependence of the data indicators. Three simulation examples are given to demonstrate the proposed algorithm's effectiveness. Furthermore, the performances of these approaches are analyzed, including parameter estimation of RMSE, parameter sparsity and prediction of state and output result.