In this paper, we introduce a new model for RF-powered cognitive radio networks with the aim to improve the performance for secondary systems. In our proposed model, when the primary channel is busy, the secondary transmitter is able either to backscatter the primary signals to transmit data to the secondary receiver or to harvest RF energy from the channel. The harvested energy then will be used to transmit data to the receiver when the channel becomes idle. We first analyze the tradeoff between backscatter communication and harvest-then-transmit protocol in the network. To maximize the overall transmission rate of the secondary network, we formulate an optimization problem to find time ratio between taking backscatter and harvest-then-transmit modes. Through numerical results, we show that under the proposed model can achieve the overall transmission rate higher than using either the backscatter communication or the harvest-then-transmit protocol.