This work studied the concept of a bornological algebra using a metric focus. The theory of bornological algebra generalizes from the metric space structures to the bornological set setting. The construction of this set allows us to expand the frame of the metrizability of algebras by developing these algebras using tools of the bornological and metrical language simultaneously. In this work, we improve the notion of metrizable bornological algebra and introduce many essential constructions in the class of bornological algebra.