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Modern distribution power system has become a typical cyber-physical system (CPS), where reliable automation control process is heavily depending on the accurate measurement data. However, the cyber-attacks on CPS may manipulate the measurement data and mislead the control system to make incorrect operational decisions. Two types of cyber-attacks (e.g., transient cyber-attacks and steady cyberattacks) as well as their attack templates are modeled in this paper. To effectively and accurately detect these false data injections, a multivariate Gaussian based anomaly detection method is proposed. The correlation features of comprehensive measurement data captured by micro-phasor measurement units (μPMU) are developed to train multivariate Gaussian models for the anomaly detection of transient and steady cyberattacks, respectively. A k-means clustering method is introduced to reduce the number of μPMUs and select the placement of μPMUs. Numerical simulations on the IEEE 34 bus system show that the proposed method can effectively detect the false data injections on measurement sensors of distribution systems.