The financial risk evaluation is critically vital for enterprises to identify the potential financial risks, provide decision basis for financial risk management, and prevent and reduce risk losses. In the case of considering financial risk assessment, the basic problems that arise are related to strong fuzziness, ambiguity and inaccuracy. q-rung orthopair fuzzy set (q-ROFS), portrayed by the degrees of membership and non-membership, is a more resultful tool to seize fuzziness. In this article, the novel q-rung orthopair fuzzy score function is given for dealing the comparison problem. Later, the and operations are explored and their interesting properties are discussed. Then, the objective weights are calculated by CRITIC (Criteria Importance Through Inter-criteria Correlation). Moreover, we present combined weights that reflects both subjective preference and objective preference. In addition, the q-rung orthopair fuzzy MCDM (multi-criteria decision making) algorithm based on CoCoSo (Combined Compromise Solution) is presented. Finally, the feasibility of algorithm is stated by a financial risk evaluation example with corresponding sensitivity analysis. The salient features of the proposed algorithm are that they have no counter-intuitive case and have a stronger capacity in differentiating the best alternative.