In this article, an efficient sequential linear programming algorithm (SLP) for uncertainty analysis-based data-driven computational mechanics (UA-DDCM) is presented. By assuming that the uncertain constitutive relationship embedded behind the prescribed data set can be characterized through a convex combination of the local data points, the upper and lower bounds of structural responses pertaining to the given data set, which are more valuable for making decisions in engineering design, can be found by solving a sequential of linear programming problems very efficiently. Numerical examples demonstrate the effectiveness of the proposed approach on sparse data set and its robustness with respect to the existence of noise and outliers in the data set.