This paper presents a design for an integrated all-optical convolution neural network in which all three network layers i.e. convolution, max-pooling and fully connected can be implemented in silicon photonics platform with the use of GST-based active waveguides. In the convolution layer the need for the ReLU is mitigated by using positive kernel values. Also, the designed max-pooling layer is completely based on silicon photonics elements and requires no electrical or electro-optical logical element. These significantly reduce the overall network complexity. The individual optical elements, network layers and the overall convolution network are simulated using finite-difference time-domain method, coupled mode theory and Python programming, respectively. The network performance is evaluated in MNIST data classification and also signal modulation identification (RML2016.10a dataset) which showed accuracies of 91.90% and 80%, respectively. These are comparable to the highest-reported values for the convolution networks while the proposed network has a less complex design and can be completely implemented with integrated optical elements.