Cardiovascular disease, especially hypertension, has become one of the biggest killers of human life and health. Therefore, early detection and prevention of cardiovascular diseases are of great significance for people’s health. In this paper, we explore the relationship between aortic valve heart sound signal and blood pressure, and propose a method of non-invasively estimating blood pressure based on heart sound signals. First, according to the relationship between blood pressure and the heart sound signal, both the time interval between the peak point of the first heart sound and that of the second heart sound and the kurtosis of the second heart sound are extracted as features. Then the time interval between the first heart sound and the second heart sound, and the kurtosis of the second heart sound are linearly fitted to the measured blood pressure. Finally, according to the linear relationship between heart sound and blood pressure, a blood pressure evaluation formula based on the heart sound is established. The experimental results show that the time interval between the peak point of the first heart sound and that of the second heart sound, and the kurtosis of the second heart sound can be used as the characteristic parameters of blood pressure evaluation, which have a good linear relationship with blood pressure. The goodness of fit is 0.801 and 0.765, separately. The average error between the blood pressure calculated from the blood pressure calculation formula and the blood pressure measured by a commercial electronic sphygmomanometer is less than 5 mmHg, and the standard deviation is less than 8 mmHg. For hypertensive patients, the time interval between the peak point of the first heart sound and the second heart sound is shortened, and the kurtosis of the second heart sound is increased, which is a typical feature of heart sounds in patients with hypertension. Compared with the traditional blood pressure calculation method, the blood pressure assessment method proposed in this paper only needs to collect heart sound signals to effectively assess the blood pressure. The method is convenient to operate and can be used for continuously monitoring the blood pressure, and is especially suitable for monitoring the blood pressures of infants, disabled patients with limbs, and disabilities in certain medical environments.