This paper proposes to remotely estimate a human subject's blood pressure using a millimeter-wave radar system. High blood pressure is a critical health threat that can lead to diseases including heart attacks, strokes, kidney disease, and vision loss. The commonest method of measuring blood pressure is based on a cuff that is contact-based, non-continuous, and cumbersome to wear. Continuous remote monitoring of blood pressure can facilitate early detection and treatment of heart disease. This paper investigates the possibility of using millimeter-wave frequency-modulated continuous-wave radar to measure the heart blood pressure by means of pulse wave velocity (PWV). PWV is known to be highly correlated with blood pressure, which can be measured by pulse transit time. We measured PWV using a two-millimeter wave radar focused on the subject's chest and wrist. The measured time delay provided the PWV given the length from the chest to the wrist. In addition, we analyzed the measured radar signal from the wrist because the shape of the pulse wave purveyed information on blood pressure. We investigated the area under the curve (AUC) as a feature and found that AUC is strongly correlated with blood pressure. In the experiment, five human subjects were measured 50 times each after performing different activities intended to influence blood pressure. We used artificial neural networks to estimate systolic blood pressure (SBP) and diastolic blood pressure (SBP) with both PWV and AUC as inputs. The resulting root mean square errors of estimated blood pressure were 3.33 mmHg for SBP and 3.14 mmHg for DBP.