For the stochastic configuration network(SCN), it randomly produces the hidden parameters and adaptively selects their scopes using an inequality constraint. As a result, the SCN exhibits superior performance in convergence speed and modeling accuracy. It is inevitable to produce low-value and redundant hidden nodes due to the inherent feature of a randomized algorithm. To improve the sparsity of the SCN soft sensor model, a parsimonious stochastic configuration network(PSCN) is proposed in this paper. The $L_1$ norm is plugged into the cost function of the PSCN, and a new inequality constraint is built to obtain the high-quality hidden nodes. Next, considering the non-smoothness and non-convexity of the cost function with $L_1$ norm, the alternating direction method of multipliers(ADMM) is employed to update the output weights of the whole network. Finally, the proposed method is applied to benchmark data sets and soft measurement issue in industrial process, and simulation results show that it can effectively simplify the network structure and possess the higher generalization.