The vulnerability of GNSS to spoofing attacks has received much attention in recent years. Among various spoofing techniques, replay attack is a typical and common one due to its simplicity and effectiveness. To detect and mitigate spoofing threats including the replay spoofing, a new anti-spoofing method is proposed. Specifically, a Doppler measurements based positioning method has been adopted for checking the position consistency with the pseudorange measurements based positioning, which is the standard positioning method currently. The theoretical base of this proposed method has been analyzed. Grounded on the theory, a practical algorithm of this anti-spoofing method has been achieved. By comparing with the standard positioning receiver, both the simulation outcomes and the real-time experimental results proved the feasibility and effectiveness of the proposed method.