Laguerre-Gaussian (LG) modes, carrying the orbital angular momentum of light, are critical for important applications, such as high-capacity optical communications, superresolution imaging, and multidimensional quantum entanglement. Advanced developments in these applications demand reliable and tunable LG mode laser sources, which, however, do not yet exist. Here, we experimentally demonstrate highly efficient, highly pure, broadly tunable, and topological-charge-controllable LG modes from a Janus optical parametric oscillator (OPO). The Janus OPO featuring a two-faced cavity mode is designed to guarantee an efficient evolution from a Gaussian-shaped fundamental pump mode to a desired LG parametric mode. The output LG mode has a tunable wavelength between 1.5 and 1.6 μm with a conversion efficiency >15 % , a controllable topological charge up to 4, and a mode purity as high as 97%, which provides a high-performance solid-state light source for high-end demands in multidimensional multiplexing/demultiplexing, control of spin-orbital coupling between light and atoms, and so on.