Number of inseminations to conception (NINS), an important fertility trait, requires appropriate approaches for genetic evaluation due to its non-normal distribution and censoring records. In this study, we analyzed NINS in 474837 Danish Holstein cows at their first lactation by using seven models which deal with the categorical phenotypes and censored records in different manners, further assessed these models with regard to stability, lack of bias and accuracy of prediction. The estimated heritability from four models based on original NINS specified as a linear Gaussian model, categorical threshold model, threshold linear model and survival model were similar (0.031-0.037). While for the other three models based on the binary response derived from NINS, referred as threshold model (TM), logistic and probit models (LOGM and PROM), the heritability were estimated as 0.027, 0.063 and 0.027, respectively. The model comparison concluded that different models could lead to slightly different sire rankings in terms of breeding values; a more complicated model led to less stability of prediction; the models based on the binary response derived from NINS (TM, LOGM and PROM) had slightly better performances in terms of unbiased and accurate prediction of breeding values.