A novel deep learning (DL) based channel estimation method is proposed for full-duplex backscatter communication systems to realize the wireless-powered sensor networks (WPSN) for internet of things (IoT). We aim to minimize the power consumption at a sensor node by reflecting the supplied power signal from an access point (AP), which is called backscatter communication. Moreover, by adopting the frequency-shifted modulation technique during backscatter transmission, full-duplex communication is performed between the AP and the sensor node. However, this incurs a problem that the uplink and downlink channels are cascaded, which results in degrading the performance of beamforming. In order to overcome this problem, we propose a novel channel estimation method that extracts separate uplink and downlink channels from the cascaded channels. We formulate the problem for joint channel estimation and pilot optimization, and then design the DL based channel estimator, which is composed of feedforward neural network(FNN) and convolutional neural network(CNN), for compensating nonlinearity and non-convexity. Finally, we analyze the performance of the proposed DL based channel estimator compared to the conventional channel estimator.