This talk focus on optimality conditions of nonsmooth sparsity multiobjective optimization problem (shortly, SMOP) by the advanced variational analysis. We present the variational analysis characterizations, such as tangent cones, normal cones, dual cones, second-order tangent set and support function, of the sparse set, and give the relationships among the sparse set and its tangent cones and second-order tangent set. The first-order necessary conditions for local weakly Pareto efficient solution of SMOP are established under some suitable conditions. We also obtain the equivalence between basic feasible point and stationary point defined by the Fr\'{e}chet normal cone of SMOP. The sufficient optimality conditions of SMOP are derived under the pseudoconvexity. The second-order optimality conditions of SMOP are established by the Dini directional derivatives of the objective function and the Bouligand tangent cone and second-order tangent set of the sparse set.