Bayesian methods are useful for statistical inference. However, real-world problems can be challenging using Bayesian methods when the data analyst has only limited prior knowledge. In this paper we consider a class of problems, called partial Bayes problems, in which the prior information is only partially available. Taking the recently proposed inferential model approach, we develop a general inference framework for partial Bayes problems, and derive both exact and efficient solutions. In addition to the theoretical investigation, numerical results and real applications are used to demonstrate the superior performance of the proposed method.