Aims. We present optical and near-infrared (NIR) photometry of supernova (SN) 2008fv and a brief investigation of SN type Ia to search for possible correlations between the properties of NIR light curves and the optical decline rate. Methods. We analyse our BVRI and JHK observations to derive light curves (LCs), colour curves, and the bolometric behaviour of SN 2008fv. Data range from about five days before to two months after maximum. We also collect a database of the main characteristics of NIR LCs of SNe Ia available in literature. Results. We find close similarities between the observed LCs of the SN event studied here and SN 2000E. SN 2008fv is a slow-declining SNe Ia with a post-maximum decline of Δm 15,B = 0.96 ± 0.08 mag and a B-band maximum luminosity of M B,0 = −19.40 ± 0.1 mag, close to the value of normal SNe Ia. The optical and NIR data allow us to constrain the host galaxy reddening of NGC 3147, E(B−V) = 0.22 ± 0.05 mag and its distance μ = 33.2 ± 0.1 mag. Furthermore, we derive a synthesized 56 Ni mass of about 0.7 M , by using the well-known relation between the maximum luminosity of the uvoir bolometric light curve and the initial content of 56 Ni. We investigate the correlation between the NIR characteristics of LCs and optical properties by collecting data of a sample of 40 SNe. We derive quantitative relationships involving the epoch of the secondary maximum in the JHK bands and the decline rate Δm 15 (B). Further, we find no correlations between Δm 15 measured in the JHK bands and the optical Δm 15 (B). In contrast, quite evident correlations with the Δm 15 (B) and Δm 40 (J)/Δm 15 (H).