This paper reports a new modular phalanx which possesses the capabilities of suction adhesion and adjustable stiffness for grasping tasks. The presented membrane-suction hole patterned layer can generate sufficient suction force to grasp objects with large radius of curvature and weight. Variable-stiffness of the phalanx tuned by granular jamming structure considerably enhances the grasping robustness and lifting force. Suction-lift capability and adjustable constrained stiffness are analytically modeled and experimentally validated by suction and constraint force tests on the fabricated prototype. Through various grasping demonstrations, the objects with a radius of 5 cm and thin plates are successfully suction-picked. The proposed soft phalanges are further integrated in articulated and parallel grippers to show their augmentation in motion sequence (picking thin object) and grasping stability (improving 1.35 times in lifting and preventing slip) over conventional grippers.