This paper proposes the technique which can improve the data rate of secondary system in radio frequency (RF) powered backscatter cognitive radio networks (CRNs). In previous studies, secondary system cannot transmit data by conventional radio transmission when a channel is busy. However, in our proposed scheme, secondary transmitter (ST) is allowed to transmit data even though the channel is busy. The ST selects the harvest-then-transmit or backscatter mode based on interference at primary receiver (PR). We obtain the maximum data rate of secondary system by optimizing the allocated time of energy harvesting, transmitting and backscattering. We evaluate the performance of proposed scheme through the simulation. The results show the proposed scheme improves the performance of the secondary system in terms of throughput.