We introduce process-oriented programming as a natural extension of object-oriented programming for parallel computing. It is based on the observation that every class of an object-oriented language can be instantiated as a process, accessible via a remote pointer. The introduction of process pointers requires no syntax extension, identifies processes with programming objects, and enables processes to exchange information simply by executing remote methods. Process-oriented programming is a high-level language alternative to multithreading, MPI and many other languages, environments and tools currently used for parallel computations. It implements natural object-based parallelism using only minimal syntax extension of existing languages, such as C++ and Python, and has therefore the potential to lead to widespread adoption of parallel programming. We implemented a prototype system for running processes using C++ with MPI and used it to compute a large three-dimensional Fourier transform on a computer cluster built of commodity hardware components. Three-dimensional Fourier transform is a prototype of a data-intensive application with a complex data-access pattern. The process-oriented code is only a few hundred lines long, and attains very high data throughput by achieving massive parallelism and maximizing hardware utilization.