Hybrid fuzzing, combining symbolic execution and fuzzing, is a promising approach for vulnerability discovery because each approach can complement the other. However, we observe that applying hybrid fuzzing to kernel testing is challenging because the following unique characteristics of the kernel make a naive adoption of hybrid fuzzing inefficient: 1) having indirect control transfers determined by system call arguments, 2) controlling and matching internal system state via system calls, and 3) inferring nested argument type for invoking system calls. Failure to handling such challenges will render both fuzzing and symbolic execution inefficient, and thereby, will result in an inefficient hybrid fuzzing. Although these challenges are essential to both fuzzing and symbolic execution, to the best of our knowledge, existing kernel testing approaches either naively use each technique separately without handling such challenges or imprecisely handle a part of challenges only by static analysis. To this end, this paper proposes HFL, which not only combines fuzzing with symbolic execution for hybrid fuzzing but also addresses kernel-specific fuzzing challenges via three distinct features: 1) converting indirect control transfers to direct transfers, 2) inferring system call sequence to build a consistent system state, and 3) identifying nested arguments types of system calls. As a result, HFL found 24 previously unknown vulnerabilities in recent Linux kernels. Additionally, HFL achieves 15% and 26% higher code coverage than Moonshine and Syzkaller, respectively, and over kAFL/S2E/TriforceAFL, achieving even four times better coverage, using the same amount of resources (CPU, time, etc.). Regarding vulnerability discovery performance, HFL found 13 known vulnerabilities more than three times faster than Syzkaller. 1 The discussion throughout this paper particularly focuses on the Linux kernel, but most of descriptions and knowledge can be generally applied to other kernels as well. If not mentioned specifically, the kernel implicates the Linux kernel in this paper.