The presence of a cavity in a protoplanetary disk revealed by dust continuum emissions is sometimes postulated as a signpost of an embedded gas giant planet. More peculiarly, dust emissions exterior to the cavity are often observed to be asymmetric. We explore the possibility of the asymmetry as a result of the asymmetric distribution of dust in an eccentric protoplanetary disk under the secular gravitational perturbation of an embedded massive gas giant planet. We find that the surface density of the dust well coupled to the disk gas is enhanced around the apocenter of the disk. In addition, the azimuthal distributions of particles of various sizes can deviate significantly due to different coupling to the gas. Overall, the asymmetric structure exhibits a phase correlation between the gas velocity field and dust density distribution. A Doppler map for an eccentric disk is also presented based on Cycle 1 ALMA observations. Our study potentially provides a reality check as to whether an asymmetric disk gap detected at sub-mm and cm wavelengths is a signpost of a massive gas giant planet.