Softwarized networks are expected to be utilized as a core network for the 5th Generation (5G) mobile services. For the mobile core network architecture, service chaining is expected to be utilized for dynamically steering traffic across multiple network functions. In this paper, for dynamic multipath service chaining, we propose a greedy-based VNF placement algorithm. This method can provide multipath service chaining so as to utilize the node resources such as CPU effectively while decreasing the cost about bandwidth and transmission delay. The proposed algorithm consists of four difference algorithms, and VNFs are placed appropriately with those algorithm. Our proposed algorithm obtains near optimal solution for the formulated optimization problem with a greedy algorithm, and hence multipath service chains can be provided dynamically. We evaluate the performance of our proposed method with simulation and compare its performance with the performances of other methods. In numerical examples, it is shown that our proposed algorithm can provide multipath service chains appropriately so as to utilize the limited amount of node resources effectively. Moreover, it is shown that our proposed algorithm is effective for providing service chaining dynamically in large-scale network.