Random lasing with coherent feedback is detected in the array of vertical ZnO nanorods synthesized on a Si(100) substrate. Under high-intensity optical pumping at the wavelength of 337.1 nm at room temperature, several narrow laser peaks with the width of 0.1 nm are observed in the wavelength region around 392 nm. The laser radiation is emitted in a direction orthogonal to the axis of the nanorods. Study of the behavior of the laser spectrum with the excited area shows good agreement of the data with the theory of random lasers. The mechanism of laser emission is related to the formation of closed paths of light due to multiple coherent scattering at the vertically oriented ZnO nanorods.