Our present study is focused on using a machine learning approach for alloy design, especially in identifying compositions of niobium alloys, which are not known before. Here, we have utilized a Bayesian optimization algorithm to guide us in searching for optimized Nb-based quinary and quaternary alloy compositions for targeted mechanical properties. Here, we first trained the machine learning model, using a database populated with experimental property data for several Nb alloys, to map the alloy composition with the mechanical properties such as yield strength (YS) and ultimate tensile strength (UTS). We created over a million virtual quaternary and quinary alloy compositions as candidates considering different alloying elements with varying weight percentage values. We utilized the trained machine learning model to predict the mechanical property and quantified the uncertainty for each candidate available in the virtual space. We then calculated the expected improvement (EI) value for each candidate and used this metric to screen for suitable alloy compositions from the virtual candidates. Furthermore, for multi-objective optimization of both YS and UTS simultaneously, we created a single integrated property by combining both the properties into one composite property.