This paper proposes a traveling-wave endfire antenna with temporal differentiation function, which is able to directly demodulate a frequency modulated signal at the antenna end. To tailor the frequency response as a differentiator, aperiodic phase loading technique is proposed to design such a multifunctional endfire antenna. Space mapping technique is also adopted in the final tuning process. To verify the proposed design technique, an illustrative example of differentiating endfire antenna is designed and fabricated. The results show that it works within 15.1-15.7 GHz with differentiation capability, and achieves an endfire gain of 17.3 dBi at center frequency. To verify its differentiation function, a frequency modulated signal is radiated by the other standard horn antenna to the designed differentiating antenna. The directly demodulated signal agree well with the ideal transmitted one, which finally validate the proposed technique.