Land desertification caused by human over-exploitation and destruction of nature has become one of the severest ecological problems of China inland basin. In order to learn about the situation of the sustainable growth of plants in desertification areas, we establish a new water-plant model with stochastic effects to study the effect of the random water supply on plant growth in this paper. Through phase diagram analysis and It$\hat{\rm o}$ formula, we prove the global existence of the positive solution for water-plant stochastic model. By the average integral method, It$\hat{\rm o}$ formula and the strong large numbers law of local martingales, we obtain the sufficient conditions for the strong persistence in the mean of plants. The numerical simulations show the effect of the random water supply on plant growth. The results of theoretical and numerical simulations provide the theoretical basis for the control over the desertification problem.