In order to achieve fingerprint location based on the strength of low energy bluetooth received signal, a new fingerprint location method is proposed, which does not need to collect too many data points to establish fingerprint database and can correct the positioning error in time. In the off-line phase, we use the low rank matrix completion theory to recover the fingerprint database with only a small number of acquisition points to reduce the workload. In the online stage, after clustering and matching the fingerprint database, the localization problem is transformed into compressed sensing model to improve positioning accuracy. Experimental results show that the proposed positioning algorithm can effectively reduce about 40% workload of early data acquisition and reduce the positioning error from 0.93 m to 0.71 m.