The purpose of this study was to examine the impact of dimensionality, common-item set format, and different scale linking methods on preserving equity property with mixed-format test equating. Item response theory (IRT) true-score equating (TSE) and IRT observed-score equating (OSE) methods were used under common-item nonequivalent groups design. The equity property was evaluated based on first-order equity (FOE) and second-order equity (SOE) properties. A simulation study was conducted based on actual item parameter estimates obtained from the TIMSS 2011 8th grade mathematics assessment. The results showed that: (i) The FOE and SOE properties were best preserved under the unidimensional condition, were poorly preserved when the degree of multidimensionality was severe. (ii) The TSE and OSE results, which were provided by using a mixed-format common-item set, preserved FOE better compared to equating results, which provided only a multiple-choice common item set. (iii) Under the unidimensional and multidimensional test structure, characteristic curve methods performed significantly better than moment scale linking methods in terms of preserving FOE and SOE properties.