In order to meet the explosive traffic demand, the capacity of Long Term Evolution(LTE) system needs to be further expanded, and one choice is to integrate unlicensed carrier into the overall LTE system. However, unlicensed band might be shared by other communication systems like Wi-Fi and radar, so the available bandwidth for each user could not be guaranteed. We propose a carrier aggregation resource allocation (CARA) algorithm to maximize the system utility on both licensed and unlicensed band, where the sub-carriers and data rate to users are optimized. Specifically, subcarrier allocation scheme among users is obtained by using Karush-Kuhn-Tucker(KKT) condition on the primary carrier of the licensed band in the first step. And based on this, an iterative algorithm is proposed on unlicensed band to calculate the optimal data rate for user equipment(UE) in the second step. Then the eNodeB could determine the bandwidth on unlicensed band for UEs accordingly. The simulation results show that our CARA algorithm could increase the system utility significantly compared to the conventional algorithms.