Java virtual machine (JVM) is a core technology, whose reliability is critical. Testing JVM implementations requires painstaking effort in designing test classfiles (∗.class) along with their test oracles. An alternative is to employ binary fuzzing to differentially test JVMs by blindly mutating seeding classfiles and then executing the resulting mutants on different JVM binaries for revealing inconsistent behaviors. However, this blind approach is not cost effective in practice because most of the mutants are invalid and redundant. This paper tackles this challenge by introducing classfuzz, a coverage-directed fuzzing approach that focuses on representative classfiles for differential testing of JVMs' startup processes. Our core insight is to (1) mutate seeding classfiles using a set of predefined mutation operators (mutators) and employ Markov Chain Monte Carlo (MCMC) sampling to guide mutator selection, and (2) execute the mutants on a reference JVM implementation and use coverage uniqueness as a discipline for accepting representative ones. The accepted classfiles are used as inputs to differentially test different JVM implementations and find defects. We have implemented classfuzz and conducted an extensive evaluation of it against existing fuzz testing algorithms. Our evaluation results show that classfuzz can enhance the ratio of discrepancy-triggering classfiles from 1:7% to 11:9%. We have also reported 62 JVM discrepancies, along with the test classfiles, to JVM developers. Many of our reported issues have already been confirmed as JVM defects, and some even match recent clarifications and changes to the Java SE 8 edition of the JVM specification.