The fast-response and high-sensitivity surface acoustic wave sensor based on the hematoporphyrin (Hp) layer–lithium niobate (LiNbO3) structure has been investigated. The amplitude and phase of the Hp–LiNbO3 SAW delay line output signal were measured as functions of relative humidity (RH) at the steady-state conditions and as functions of time upon the step-like RH variation. Both the SAW attenuation and velocity strongly depend on the relative humidity (RH) due to water sorption by Hp film. At SAW frequency 86 MHz, the changes of −0.8 dB in SAW transmission loss and −3° in phase per 1% of RH were obtained, corresponding to 110 ppm/1% RH in relative SAW velocity change and 1.23 × 10−3 per 1% RH in the change in the SAW attenuation per wavelength. The sensor exhibits fast response to the step jump up in humidity and fast recovery upon the abrupt humidity drop down with characteristic times of about 1 s. The applicability of the sensor for human breath monitoring is demonstrated.