Recently, non-contact blood pressure measurement is attracting increasing interests because it is suitable for the blood pressure measurement on a daily basis. A Doppler radar is a key device to enable the non-contact blood pressure measurement, and it can observe pulse waves due to aortic vasomotion. Specifically, PTT (Pulse Transit Time) is known to be correlated with the blood pressure, and thus the blood pressure can be measured by calculating the PTT from the pulse waves. However, to avoid the effects of slight body movements and breathing, the conventional method requires the subject to lie down on a bed and to stop breathing. In this paper, we propose a Doppler radar-based blood pressure measurement method that works against a subject with slight body movements and breathing. Due to respiration and slight body movements, the pulse wave could be distorted, which makes it difficult to calculate PTT. To solve this issue, in the proposed method, by relating features of the distorted pulse wave to those of the clean pulse wave using a deep learning model with LSTM (Long Short-Term Memory), the distorted pulse wave is transformed to a clean pulse wave that provides PTT correlated with the blood pressure strongly. The experimental results showed that PTT calculated using the proposed method has a strong correlation with actual blood pressure and the accuracy of blood pressure estimation is improved, compared with the conventional method.