Floating-point arithmetic is widely used in applications from several fields including scientific computing, machine learning, graphics, and finance. Many of these applications are rapidly adopting the use of GPUs to speedup computations. GPUs, however, have limited support to detect floating-point exceptions, making it difficult to software developers to detect unexpected exceptional cases in such applications. We present FPChecker, the first tool to automatically detect floating-point exceptions in GPU applications. FPChecker uses the clang/LLVM compiler to instrument GPU kernels and to detect floating-point exceptions in GPUs at runtime. Once an exception is detected, it reports to the programmer the code location of the exception as well as other useful information. The programmer can then use this information to avoid the exception, e.g., by modifying the application algorithm or changing its input. We present the design of FPChecker, an evaluation of the overhead of the tool, and a real-world case scenario on which the tool is used to identify a hidden exception. The slowdown of FPChecker is moderate ($1.5\times$ on average) and the code is publicly available as open source.