Malicious users can exploit vulnerabilities in cognitive radio networks (CRNs) and cause heavy performance degradation by denial of service (DoS) attacks. During operation, cognitive radios (CRs) spend a considerable amount of time to identify idle (free) channels for transmission. In addition, CRs also need additional security mechanisms to prevent malicious attacks. Proactive model predictive control (MPC)-based medium access control (MAC) protocols for CRs can quicken the idle channel identification by predicting future states of channels in advance. This provides enough time for CRs to carry out other calculations like DoS attack detection. However, such external detection techniques use additional power that makes them inappropriate for energy constrained applications. As a solution, this paper proposes a proactive learning-based MAC protocol (PROLEMus) that shows immunity to two prominent CR-based DoS attacks, namely, primary user emulation attack (PUEA) and spectrum sensing data falsification (SSDF) attack, without any external detection mechanism. PROLEMus shows an average of 6.2%, 8.9%, and 12.4% improvement in channel utilization, backoff rate, and sensing delay, respectively, with low prediction errors (≤1.8%) saving 19.65% energy, when compared to recently proposed MAC protocols like ProMAC aided with additional DoS attack detection mechanism.