Photometric and spectroscopic observations of a slowly declining, luminous type Ia supernova (SN Ia) 2011hr in the star-burst galaxy NGC 2691 are presented. SN~2011hr is found to peak at MB=−19.84±0.40mag, with a post-maximum decline rate Δm15(B) = 0.92 ± 0.03\,mag. From the maximum-light bolometric luminosity, L=(2.30±0.90)×1043ergs−1, we estimate the mass of synthesized \Nifs\ in SN~2011hr to be M(\rm{^{56}Ni})=1.11 \pm 0.43\,M_{\sun}. SN 2011hr appears more luminous than SN 1991T at around maximum light, and the absorption features from its intermediate-mass elements (IMEs) are noticeably weaker than the latter at similar phases. Spectral modelling suggests that SN 2011hr has the IMEs of ∼\,0.07 M_{\sun} in the outer ejecta, which is much lower than the typical value of normal SNe Ia (i.e., 0.3 -- 0.4 M_{\sun}) and is also lower than the value of SN 1991T (i.e., ∼\,0.18 M_{\sun}). These results indicate that SN~2011hr may arise from a Chandrasekhar-mass white dwarf progenitor that experienced a more efficient burning process in the explosion. Nevertheless, it is still possible that SN~2011hr may serve as a transitional object connecting the SN 1991T-like SNe Ia with the super-luminous subclass like SN 2007if given that the latter also shows very weak IMEs at all phases