A $k$-submodular function is a generalization of a submodular function, its definition domain is extended from the collection of single subsets to the collection of $k$ disjoint subsets. The $k$-submodular maximization problem has a wide range of applications. In this paper, we propose a nested greedy and local search algorithm for the problem of maximizing a monotone $k$-submodular function subject to a knapsack constraint and $p$ matroid constraints.