The rapid developments in orbital-angular-momentum-carrying Laguerre-Gaussian (LG 0 l ) modes in recent years have facilitated progresses in optical communication, micromanipulation and quantum information. However, it is still challenging to efficiently generate bright, pure and selectable LG 0 l laser modes in compact devices. Here, we demonstrate a low-threshold solid-state laser that can directly output selected high-purity LG 0 l modes with high efficiency and controllability. Spinorbital angular momentum conversion of light is used to reversibly convert the transverse modes inside cavity and determine the output mode index. The generated LG 0 1 and LG 0 2 laser modes have purities of ~97% and ~93% and slope efficiencies of ~11% and ~5.1%, respectively. Moreover, our cavity design can be easily extended to produce higher-order Laguerre-Gaussian modes and cylindrical vector beams. Such compact laser configuration features flexible control, low threshold, and robustness, making it a practical tool for applications in super-resolution imaging, highprecision interferometer and quantum correlations.