Cognitive Networks were introduced to resolve issues by incorporating intelligence into the network functions. Hence, a hybrid algorithm was developed to improve spectrum resource allocation in a cognitive network for distributed computing. Five hundred thousand datasets were collected from Nigeria Communication Commission (NCC) repository. Artificial Neural Network was used to divide the dataset into 4 stages: UHF, FM, GSM 900 and DCS 1800. The hybrid algorithm was achieved using Hidden Markov Models (HMMs) which was combined with Markov-based Channel Prediction Algorithm (MCPA) in CN for dynamic spectrum allocation and higher efficiency of the spectrum holes to improve the accuracy. The combination of the mentioned two algorithms were simulated using MATLAB simulator 2019b for accuracy test. The result showed that the efficiency of the radio networks was found to be closed. Power efficiency increased from 76.66% to 86.82% for FM Broadcast, 76.91% to 86.82% for GSM-900, 78.19% to 89.04% for DCS-1800 and 78% to 88.55% for UHF TV. The computation results showed a level of improvement in spectrum occupancy license distribution from 19.6 to 61.1%. In conclusion, it was demonstrated that a hybrid algorithm offered a better solution in wireless networking by using an improved algorithm to provide a cognitive spectrum occupancy technique in a wireless network. It was recommended that telecommunication companies should adopt an improved algorithm for enhancing CN in their operations.