A novel design of a cognitive radar (CR) hybridized with a phased array radar (PAR) having a low probability of intercept (LPI) transmit beam forming is proposed. PAR directed high gain property reveals its position to interceptors. Hence, the PAR high gain scanned beam patterns, over the entire surveillance region, are spoiled to get the series of low gain basis patterns. For unaffected array detection performance, these basis patterns are linearly combined to synthesize the high gain beam pattern in the desired direction using the set of weight. Genetic algorithm (GA) based evolutionary computing technique finds these weights offline and stores to memory. The emerging CR technology, having distinct properties (i.e., information feedback, memory, and processing at receiver and transmitter), is hybridized with PAR having LPI property. The proposed radar receiver estimates the interceptor range and the direction of arrival (DOA), using the extended Kalman filter (EKF) and the GA, respectively, and sends as feedback to transmitter. Selector block in transmitter gets appropriate weights from memory to synthesize the high gain beam pattern in accordance with the interceptor range and the direction. Simulations and the results validate the ability of the proposed radar.