A class of parameter estimation problem is put forth with bounded data uncertainties, and solved it based on linear matrix inequalities (LMI). The uncertainties are expressed by a priori bounds on perturbations of coefficient matrix and its elements, which covers some situations explored in  and  and is a more general one. Thus, the proposed method, which based on LMI, is simple, practical, and general. We analyzed the solution, and discussed several special cases, such as selected columns are subject to perturbations. Simulation results give more details of the proposed method.