An unsupervised monocular visual odometry based on the principle of multi-view geometry and effective combination of the convolutional neural network for image depth estimation and correspondences selection is proposed. Aiming at the problem that mainstream depth estimation networks tend to lose the shallow features of images, a depth estimation network based on improved dense blocks is constructed to effectively aggregate shallow features and improve the accuracy of image depth estimation. The odometry uses the depth estimation network to accurately predict the depth of the monocular image, uses the optical flow network to obtain forward-backward optical flow, and select high-quality correspondences based on the principle of forward and backward optical flow consistency. The initial pose and calculated depth are obtained by using multi-view geometric principles and optimization methods, and a 6-degree-of-freedom pose with the fixed global scale is obtained through a specific scale alignment principle. At the same time, in order to improve the network's ability to learn scene details and the information of weak texture regions, the feature metric loss based on feature map synthesis is combined into the network loss function. On the KITTI Odometry dataset, the depth estimation under different thresholds has achieved accuracy rates of 85.9%, 95.8%, and 97.2%, and the absolute trajectory error of the odometry evaluation on the 09 and 10 sequences is 0.007m. Experimental results show the effectiveness and accuracy of the proposed method, and prove that it is superior to the existing methods on the task of visual odometry.