Terahertz holographic imaging has broad applications in the field of personal security verification, concealed weapon detection, and non-destructive testing. To suppress the range ambiguity, a fast sparse image reconstruction approach and imaging scheme is proposed for three-dimensional terahertz holography. The proposed algorithm establishes the terahertz imaging geometry and corresponding echo model. The range ambiguity is eliminated using the random step frequency method, and a frequency shift procedure is applied to recover the targets with a high computational efficiency. Simulation and experimental results verify the proposed algorithm.