A semiconductor pressure sensor comprising two pressure sensing diaphragms attached to a support frame embedded within a bonding agent joining two parts of a housing which defines therein fluid passages in communication with two pressure sensing diaphragms. The support frame includes a support plate portion and terminal portions having the inner ends embedded within the bonding agent and the outer ends projecting outwardly of the bonding agent for external connections. The support frame is formed by cutting a lead frame, which has a support frame portion, terminal portions and a surrounding frame integrally connected together, substantially along the outer contour of the housing except for the terminals. A method for manufacturing the pressure sensor is also disclosed.