In order to obtain clean members of the open cluster NGC 6819, the proper motions and radial velocities of 1691 stars are used to construct a three-dimensional (3D) velocity space. Based on the DBSCAN clustering algorithm, 537 3D cluster members are obtained. From the 537 3D cluster members, the average radial velocity and absolute proper motion of the cluster are Vr=+2.30+/-0.04km/s and (PMRA, PMDE)=(-2.5+/-0.5, -4.3+/-0.5)mas/yr, respectively. The proper motions, radial velocities, spatial positions and color-magnitude diagram of the 537 3D members indicate that our membership determination is effective. Among the 537 3D cluster members, 15 red clump giants can be easily identified by eye and are used as reliable standard candles for the distance estimate of the cluster. The distance modulus of the cluster is determined to be (m-M)0=11.86+/-0.05mag (2355+/-54pc), which is quite consistent with published values. The uncertainty of our distance modulus is dominated by the intrinsic dispersion in the luminosities of red clump giants (~0.04mag).