We present an extensive analysis of the relationship between star formation rate surface density (ΣSFR) and molecular gas surface density (ΣH2) at sub-kpc scale in the elliptical galaxy Centaurus A (also known as NGC 5128) at the distance 3.8 Mpc. 12CO (J = 2-1) data from Atacama Large Millimetre/Sub-Millimetre Array SV data with very high resolution (2.9′′, 0.84′′), as well as 24 μm data from the Spitzer Space Telescope, were used. This is one of the first studies of the SF law on Centaurus A at this very high spatial resolution. The results showed a breakdown in star formation law with a 0.49±0.05 index relating ΣSFR and ΣH2 at 185 pc. A significant correlation exists between surface densities of molecular gas and SFR with very long depletion time (68 Gy). In addition we examined the spatially resolved relationship between velocity dispersion and star formation rate surface density for the outer disk of this galaxy and we found that the average velocity dispersion is equal to 11.78 km/s. The velocity dispersion of the molecular ISM for the outer disk is found to follow a power relation with the star formation rate surface density σ∝ΣSFRβ, where β is the slope from the ordinary least square fitting. The value of β is about 1/n≈2.16±0.40 and n is the power law index of the star formation law.