Phase wrapping is a major problem in direction-of-arrival (DOA) estimation using phase-difference observations. For an antenna pair with an inter-antenna spacing greater than half of the wavelength (λ/2) of the signal, phase wrapping occurs at certain DOA angles leading to phase-difference ambiguities. Existing phase unwrapping methods exploit either frequency or spatial diversity. These techniques work by imposing restrictions on the utilized frequencies or the receiver array geometry. In addition to these restrictions, sensitivity to noise and calibration errors is another limitation of these methods. We propose a grid-less phase-difference projection (PDP) DOA algorithm to overcome these issues. The concept of wrapped phased-difference pattern (WPDP) is introduced, which allows us to compute most of the parameters required for DOA estimation in an offline manner. This results in a superior computational speed in real-time compared to methods with similar DOA estimation performance. Simulation results demonstrate the excellent performance of the proposed algorithm, both in terms of accuracy and speed.