Thermophilic fungi produce thermostable enzymes which have a number of applications, mainly in biotechnological processes. In this work, we describe the characterization of a protease produced in solid-state (SSF) and submerged (SmF) fermentations by a newly isolated thermophilic fungus identified as a putative new species in the genus Myceliophthora. Enzyme-production rate was evaluated for both fermentation processes, and in SSF, using a medium composed of a mixture of wheat bran and casein, the proteolytic output was 4.5-fold larger than that obtained in SmF. Additionally, the peak of proteolytic activity was obtained after 3 days for SSF whereas for SmF it was after 4 days. The crude enzyme obtained by both SSF and SmF displayed similar optimum temperature at $50^{circ}C$, but the optimum pH shifted from 7 (SmF) to 9 (SSF). The alkaline protease produced through solid-state fermentation (SSF), was immobilized on beads of calcium alginate, allowing comparative analyses of free and immobilized proteases to be carried out. It was observed that both optimum temperature and thermal stability of the immobilized enzyme were higher than for the free enzyme. Moreover, the immobilized enzyme showed considerable stability for up to 7 reuses.