Rare-earth titanate pyrochlores have attracted considerable attention for their unique magnetic frustration. Among those compounds, Yb2Ti2O7, a candidate for quantum spin ice, has been extensively studied in its magnetic ground state. However, works on its dielectric property and structure-property relationship lag far more behind. Here, by preparing and investigating nonstoichiometric Yb2-xTi2O7-δ (x = 0-0.15) ceramics, we demonstrate that the samples with x ≤ 0.05 maintain a single-pyrochlore phase, but the nonstoichiometry arouses significant structural distortion and increased oxygen vacancy. As a result, the ferromagnetism, indicated by a positive Curie-Weiss temperature, decreases almost linearly with increasing x value. Remarkably composition-dependent low-temperature dielectric relaxations have been observed. In addition, through introducing nonstoichiometry, the relaxor degree of dielectric behavior is enhanced, and the dielectric curve shows an altered shape. The origin of this dielectric relaxation is attributed to the increased structural distortion reflected by the changed bond length/angle, since there is no phase transition in 90-300 K. Our work gives a comprehensive view on the structural, magnetic, and dielectric properties of Yb2Ti2O7, which is instructive for further work on pyrochlores.