This paper examines an R D model with uncertainty from the population growth, which is a stochastic cooperative Lotka-Volterra system, and obtains a sufficiently condition for the existence of the globally positive solution. The long-run growth rate of the economic system is ultimately bounded in mean and its fluctuation of growth will not be faster than the polynomial growth. When uncertainty of the population growth, in comparison with its expectation, is sufficiently large, the growth rate of the technological progress and the capital accumulation will converge to zero. Inversely, when uncertainty of the population growth is sufficiently small or its expected growth rate is sufficiently high, the economic growth rate will not decay faster than the polynomial speed. This paper explicitly computes the sample average of the growth rates of both the technology and the capital accumulation in time and compares them with their counterparts in the corresponding deterministic model.