The pose estimation of uncooperative target spacecraft is a key technique in on-orbit servicing missions, among which the method based on monocular camera with low mass and power requirements has attracted widespread attention. However, monocular pose estimation methods mostly rely on the known 3D model of the target spacecraft, and non-model-based methods have low accuracy and even output the results when there is no target spacecraft in the image. In this paper, a non-model-based monocular pose estimation network for uncooperative spacecraft based on the convolutional neural network is proposed. This network uses three sub-networks to solve the problems of pose estimation and object detection. The first sub-network, called the attitude prediction sub-network, is used to predict the relative attitude of the target spacecraft by soft classification and error quaternion regression. The second sub-network, called the position regression sub-network, is used to predict the relative position of the target spacecraft by regression. The third sub-network called the object detection sub-network is used to detect the target spacecraft to determine whether the predicted pose needs to be output. The experimental results of the pose estimation of two public spacecraft demonstrate that the proposed method can effectively detect the target spacecraft and achieve better pose estimation accuracy than previous non-model-based methods.