In this paper, we investigate experimentally the effects of changing the electrolyte concentration on the emission of random lasers fabricated based on Zinc oxide nanosheets. Zinc oxide sheets are grown on FTO glasses using electrochemical deposition technique. We use Rhodamine 6G solution as the random laser gain medium. Optical feedback is provided by light multi-scattering from ZnO sheets. It is demonstrated here that size and shape of sheets and their related lasing emission change with electrolyte concentration. It is also shown that by increasing the electrolyte concentration, first the intensity of emission peak of the random laser obtained from ZnO sheets and organic dye increases and then by further increase of concentration, the emission spectrum converts from single mode sate to double one. We measure the threshold pumping energy for each of the lasing modes excited in the structure. Our results show that at first the threshold of lasing mode decreases with increase of concentration. With further increase of concentration, a new mode appears in the emission spectrum leading to increase of the threshold of old mode and decrease of its intensity.