QuTiP is open-source software for simulating the dynamics of open quantum systems. The QuTiP library depends on the excellent Numpy and Scipy numerical packages. In addition, graphical output is provided by Matplotlib. QuTiP aims to provide user-friendly and efficient numerical simulations of a wide variety of Hamiltonians, including those with arbitrary time-dependence, commonly found in a wide range of physics applications such as quantum optics, trapped ions, superconducting circuits, and quantum nanomechanical resonators. QuTiP is freely available for use and/or modification on all Unix based platforms such as Linux and Mac OSX. Being free of any licensing fees, QuTiP is ideal for exploring quantum mechanics and dynamics in the classroom. QuTiP may also be thought of as an open source alternative to the popular, but aging, Quantum Optics Toolbox (qotoolbox), although we do not aim to be in one-to-one correspondence.