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In this paper we propose Multi-objective Distributed Power Control Algorithm for Spectrum-sharing Cognitive Radios (MODPCCR). As we know that for spectrum sharing cognitive radios the most important factor is the strict limited interference caused to the primary users. Our proposed MODPCCR algorithm is able to achieve certain SINR under the strict interference power constraint to primary users, where we assume that there is no perfect channel state information (CSI) of the secondary-primary links to be provided to secondary transmitters. Implementing MODPCCR algorithm on secondary users could protect primary users and achieve certain signal to noise and interference ratio (SINR) for secondary users as well.