In this paper, a novel Doppler shift estimation method for frequency diverse array (FDA) radar based on graph signal processing (GSP) theory is proposed and investigated. First, a well-designed graph signal model for a monostatic linear FDA is formulated. Subsequently, spectral decomposition is conducted on the constructed signal model utilizing graph Fourier transform (GFT) techniques, enabling the extraction of the target’s Doppler shift parameter through spectral peak search. A comprehensive series of simulation experiments demonstrates that the proposed method can achieve the accurate estimation of target parameters even under low signal-to-noise ratio (SNR) conditions. Furthermore, the proposed method exhibits superior performance compared to the MUSIC algorithm, offering enhanced resolution and estimation accuracy. Additionally, the method is highly amenable to parallel processing, significantly reducing the computational burden associated with traditional procedures.