This paper describes the development of a handheld haptic display based on a new force perception method. The method uses periodic translational motion to create asymmetric aceleration leading to a virtual force vector. The method is based on the sigmoidal relationship between perception and physical quantities (tactile and proprioceptive sensations); humans more strongly feel rapid acceleration than slow acceleration. A prototype of the haptic display that generates one-directional force using a relatively simple mechanism is fabricated and evaluated. Experiments verify the feasibility of the proposed method by examining the effect of the frequency of acceleration and amplitude of the force on the perception of the virtual force vector.