In this work, we proposed a non-linear observer model based on convolutional neural network and compare its performance with LG-CHO for four alternative forced choice detection task using simulated breast CT images. In our network, each convolutional layer contained 3×3 filters and a leaky-ReLU as an activation function, but a pooling layer and a zero padding to the output of each convolutional layer were not used unlike general convolutional neural network. Network training was conducted using ADAM optimizer with two design parameters (i.e., network depth and width). The optimal value of the design parameter was found by brute force searching, which spanned up to 30 for depth and 128 for channel, respectively. To generate training and validation dataset, we generated anatomical noise images using a power law spectrum of breast anatomy. 50% volume glandular fraction was assumed, and 1 mm diameter signal was used for detection task. The generated images were recon- structed using filtered back-projection with a fan beam CT geometry, and ramp and Hanning filters were used as an apodization filter to generate different noise structures. To train our network, 125,000 signal present images and 375,000 signal absent images were reconstructed for each apodization filter. To measure detectability, we used percent correction with 4,000 images, generated independently from training and validation dataset. Our results show that the proposed network composed of 30 layers and 64 channels provides higher detectability than LG-CHO. We believe that the improved detectability is achieved by the presence of the non-linear module (i.e., leaky-ReLU) in the network.