The invention provides a multi-port fluid access device for medical use, such as in a blood-flow circuit during dialysis. The device has a main tubular body and a needle access port and a needleless access port located at positions axially offset from each other. Each port has a tubular body with a septum sealing the passageway to the main fluid channel of the main tubular body. Alongside the main tubular body are members providing finger-gripping surfaces at or near the axial position of the needle access port. There is also a needle shield located between the finger gripping surfaces and the needle access port. Use of the device permits either or both of needle access and needleless access to a patients blood during dialysis.