Abstract This paper leverages the big data provided by micro-phasor measurement units (μPMUs) placed along the smart distribution networks for distribution system state estimation (DSSE). We propose a novel and straightforward DSSE algorithm by solving a set of linear equations without any iterative process. The μPMUs are placed at few buses to measure the voltage phasors. The measured voltage vector is expressed as the product of current injections vector and impedance matrix of the system. Since number of μPMUs is less than number of buses, the constructed set of linear equations are underdetermined. Furthermore, the injection currents vector is sparse because any single load/generator current is negligible when compared with the total current injected from the external grid to the distribution network. Subsequently, we use Compressive Sensing and l1-norm minimization to recover the sparse current vector from the limited number of μPMUs. The voltages at all buses are obtained by multiplying the reconstructed current vector by the impedance matrix. Performance of our method is demonstrated on the IEEE 123-bus test system and a 13.8-kV, 134-bus real network with different distributed generations (DGs) penetration level and under a weakly meshed operation mode. Also, the performance of the proposed technique is compared with that of the conventional weighted least-square (WLS) method.