Broadband wavelength tunable Laguerre-Gaussian (LG) mode with flexibly manipulated topological charge is greatly desired for large-capacity optical communication. However, the operating wavelengths achieved for the current LG modes are significantly restricted either by the emission spectrum of the intracavity gain medium or by the operation wavelengths of mode-conversion or modulation components. Here, broadband wavelength-tunable LG modes with a controllable topological charge are generated based on a random fiber laser (RFL) and a digital micromirror device (DMD). The RFL can produce broadly wavelength-tunable laser emissions spanning from 1044 to 1403 nm with a high spectral purity and an excellent beam quality, benefiting from the cascaded random Raman gain starting from a ytterbium fiber based active gain. A commercially available broadband DMD is then utilized to excite the LG modes with a flexibly tunable topological charge of up to 100 order through the super-pixel wavefront shaping technique. The combination of the RFL and the DMD greatly broadens the operating wavelength region of the LG modes to be achieved, which facilitates the capacity scaling-up in the orbital angular momentum multiplexed optical communication application.