We demonstrate a semiconductor based broadband near-field superlens in the mid-infrared regime. Here, the Drude response of a highly doped n-GaAs layer induces a resonant enhancement of evanescent waves accompanied by a significantly improved spatial resolution at radiation wavelengths around λ = 20 μm, adjustable by changing the doping concentration. In our experiments, gold stripes below the GaAs superlens are imaged with a λ/6 subwavelength resolution by an apertureless near-field optical microscope utilizing infrared radiation from a free-electron laser. The resonant behavior of the observed superlensing effect is in excellent agreement with simulations based on the Drude-Lorentz model. Our results demonstrate a rather simple superlens implementation for infrared nanospectroscopy.