In today’s highly turbulent and competitive environment, the success of the organization depends on the performance of its suppliers. However, supplier selection problems are complex as they involve a large number of criteria and, frequently, some of the criteria cannot be evaluated precisely. Moreover, fluctuations of supplier performances and unknown information always exist in real-world decision-making. It is a complex multiple-criteria decision-making (MCDM) problem as it involves a trade-off among various criteria with vagueness and imprecision and also involves a group of experts with diverse opinion. Therefore, to make more practical decisions, this paper is intended to propose an integrated technique for order preference by similarity to ideal solution (TOPSIS) in fuzzy environment with multi-choice goal programming (MCGP) to handle the supplier assessment and order allocation for a battery manufacturing organization. Using linguistic variables, the decision-makers assess the rating of suppliers as well as the importance of various factors. Linguistic variables are expressed in trapezoidal fuzzy numbers (TrFN). Fuzzy-TOPSIS method is proposed to obtain the rank of suppliers and MCGP method is used to allocate suitable orders to the selected suppliers. A case study is implemented to find the applicability and validity of the proposed model. Finally, sensitivity analysis is performed to observe the effect of weights of criteria on supplier evaluation problem.