Deep Neural Networks (DNN) have been successfully used in object classification and detection. However, the computation complexity and memory requirement of DNN are high. In this paper, we propose a series of methods applied to the original VGG DNN model to reduce the complexity without sacrificing too much the accuracy in image object classification and detection. Furthermore, two compression methods, depthwise separable convolution and pruning, are employed to further reduce the numbers of weights and operations. Experimental results show that the proposed low complexity DNN models significantly reduce the number of parameters and computation complexity compared to the original VGG, GoogLeNet and ResNet-50. The proposed DNN model is also used as feature extraction in the one-stage object detection method, Single Shot Detector (SSD).