The problem of k-limited maximum base was specified into two special problems of k-limited maximum base; that is, let subset D of the problem of k-limited maximum base be an independent set and a circuit of the matroid, respectively. It was proved that under this circumstance the collections of k-limited base satisfy base axioms. Then a new matroid was determined, and the problem of k-limited maximum base was transformed to the problem of maximum base of this new matroid. Aiming at the problem, two algorithms, which in essence are greedy algorithms based on former matroid, were presented for the two special problems of k-limited maximum base. They were proved to be reasonable and more efficient than the algorithm presented by Ma Zhongfan in view of the complexity of algorithm.