The recursive algorithm for identifying the slow time-varying linear model was proposed, and its bounded convergence was analyzed. Base on the recursive algorithm, the parameters of slow time-varying linear model were proved to converge in bounded space which includes the collection of the true values of parameters. If working condition holds on, the parameters will converge to the corresponding true values with reasonable convergence factor. Generally, industrial plants can be described by slow time-varying linear model. Therefore, the model of indstrial plant can be updated in time with the recursive algorithm to track the characteristics changes effectively. As can be seen from the simulation example, the recursive algorithm can make sure that the parameters of slow time-varying linear model can be updated effectively and the output variables can be estimated accurately.