Many application scenarios require indoor positioning in fifth generation (5G) mobile communication systems in recent years. However, non-line of sight and multipath propagation lead to poor accuracy in a traditionally received signal strength-based fingerprints positioning system. In this paper, we propose a positioning method employing multivariable fingerprints (MVF) composed of measurements based on secondary synchronization signals (SSS). In the fingerprint matching, we use MVF to train the convolutional neural network (CNN) location classification model. Moreover, we utilize MVF to train the path-loss model, which indicates the relationship between the distance and the measurement. Then, a hybrid positioning model combining CNN and path-loss model is proposed to optimize the overall positioning accuracy. Experimental results show that all three positioning algorithms based on machine learning with MVF achieve accuracy improvement compared with that of Reference Signal Receiving Power (RSRP)-only fingerprint. CNN achieves best performance among three positioning algorithms in two experimental environments. The average positioning error of hybrid positioning model is 1.47 m, which achieves 9.26% accuracy improvement compared with that of CNN alone.