The Wigner quasi-probability distribution is a powerful tool for characterizing a quantum state and understanding the state dynamics in oscillators. Until now, there have been numerous measurements of this function in harmonic oscillators, and in particular in superconducting devices, however no similar measurement on anharmonic systems has been reported. We utilize the wide-range energy tunability in the multi-level Josephson phase qubit, biased in the small anharmonicity regime, to directly measure the Wigner function of various states. We demonstrate measurements of a superposition of Fock-type states, using powerful optimization algorithms for state preparation, as well as coherent-like states in this anharmonic system. This method provides an alternative to the standard state tomography techniques which usually involve a long calibration process and have limited scalability in multi-level states.