With the ever-growing number of base stations (BSs) and user equipments (UEs)in ultra-dense networks (UDN), reusing the same pilot sequences among the cells is inev-itable. With pilot reuse scheme, the channel estimation obtained at a BS contains not only the desired channel-state information (CSI)but also interference from neighboring cells,which can severely degrade CSI estimation performance and adversely affect communica-tion performance. In this paper we consider a pilot contamination avoidance based on pilot pattern design for UDN where the pilot reuse employed and the interfering users from neigh-boring cells may be not at lower power levels at the BS compared to the in-cell users. We present a novel statistical interference model of sub-carriers to describe the non-determinis-tic interference from neighboring cells. Then,we provide a pilot pattern design model with non-uniform pilot distribution. Based on this,a pilot contamination avoidance based on pilot pattern design is proposed where pilot reuse scheme and the non-deterministic interference from neighboring cells are taken into consider-ation. Unlike existing interference mitigation approaches, the proposed method eliminates interference through the method of interfer-ence avoidance and can be applied to different kinds of channel estimation algorithms. Sim-ulation results showed that the proposed ap-proach can effectively avoid the interference and ensure the accuracy of channel estimation.