The problem of high-precision indoor positioning in the 5G era has attracted more and more attention. A fingerprint location method based on matrix completion (MC-FPL) is proposed for 5G ultradense networks to overcome the high costs of traditional fingerprint database construction and matching algorithms. First, a partial fingerprint database constructed and the accelerated proximal gradient algorithm is used to fill the partial fingerprint database to construct a full fingerprint database. Second, a fingerprint database division method based on the strongest received signal strength indicator is proposed, which divides the original fingerprint database into several sub-fingerprint databases. Finally, a classification weighted K-nearest neighbor fingerprint matching algorithm is proposed. The estimated coordinates of the point to be located can be obtained by fingerprint matching in a sub-fingerprint database. The simulation results show that the MC-FPL algorithm can reduce the complexity of database construction and fingerprint matching and has higher positioning accuracy compared with the traditional fingerprint algorithm.