This study aimed to estimate genetic parameters of the linear trait genetic residual feed intake (RFI) and the ratio traits feed conversion ratio (FCR) and feed conversion efficiency (FCE) along with dry matter intake (DMI) and energy sink traits such as energy-corrected milk (ECM), body weight (BW), body condition score (BCS), and BW change (BWC) across different weeks in the first lactation of Danish Holstein cows. A second objective was to conduct a Bayesian analysis of direct and correlated superiority of the selected group when selecting on genetic RFI, FCR, or FCE. Feed intake and energy sink traits were recorded during wk 1 to 44 of lactation on 847 primiparous Danish Holstein cows. A Bayesian multivariate random regression animal model was used to analyze DMI, ECM, BW, and BCS in different weeks of lactation. Genetic RFI was obtained by conditioning DMI on ECM, BW, BCS, and BWC using genetic partial regression coefficients. The posterior distribution of the breeding values for FCR and FCE was derived from the posterior distribution of functions of “fixed” environmental effects and random additive genetic effects on DMI and ECM. Genetic superiority of the selected group was defined as the difference in additive genetic mean of the selected top individuals expected to be potential parents, and the total population after integrating genetic trends out of the posterior distribution of selection responses. Posterior means of heritability of genetic RFI ranged from 0.10 to 0.15, genetic variance of FCR and FCE ranged from 2.13 × 10⁻³ to 3.2 × 10⁻³ (kg² DMI/kg² ECM) and 6.11 × 10⁻³ to 2.4 × 10⁻² (kg² ECM/kg² DMI), respectively. Selection against RFI showed a direct response of −1.01 to −2.23 kg/d RFI and correlated responses of −0.031 to −0.056 kg/kg for FCR, 0.104 to 0.160 kg/kg for FCE, and −0.316 to −1.057 kg/d for DMI in different weeks of lactation. Selection against RFI had no significant effect on production traits but selection for ratio traits reduced BW and BCS. Posterior means of genetic correlation between DMI and ratio traits were low. In conclusion, the Bayesian procedure allowed us to estimate genetic RFI without the need for separate multiple regression analysis and considered the non-normal posterior distribution of ratio traits. Selection against genetic RFI might be an effective means to improve feed efficiency compared with ratio traits for feed efficiency in dairy cattle.