This paper presents an online data-driven algorithm to detect false data injection attacks towards synchronphasor measurements. The proposed algorithm applies density-based local outlier factor (LOF) analysis to detect the anomalies among the data, which can be described as spatio-temporal outliers among all the synchrophasor measurements from the grid. By leveraging the spatio-temporal correlations among multiple time instants of synchrophasor measurements, this approach could detect false data injection attacks which are otherwise not detectable using measurements obtained from single snapshot. This algorithm requires no prior knowledge on system parameters or topology. The computational speed shows satisfactory potential for online monitoring applications. Case studies on both synthetic and real-world synchrophasor data verify the effectiveness of the proposed algorithm.