We present the first census of giant molecular clouds (GMCs) complete down to 106 M_{sun}_ and within the inner 4 kpc of the nearest giant elliptical and powerful radio galaxy, Centaurus A. We identified 689 GMCs using CO(1-0) data with 1 arcsec spatial resolution (~20 pc) and 2 km/s velocity resolution obtained with the Atacama Large Millimeter/submillimeter Array. The I(CO)-N(H2) conversion factor based on the virial method is X_CO_ = (2 +/- 1) * 10^20 cm^-2^/(K.km/s) for the entire molecular disc, consistent with that of the discs of spiral galaxies including the Milky Way, and XCO = (5 +/- 2) * 10^20^cm^-2^/(K.km/s) for the circumnuclear disc (CND; within a galactocentric radius of 200 pc). We obtained the GMC mass spectrum distribution and find that the best truncated power-law fit for the whole molecular disc, with index {gamma} {prop.to} -2.41 +/- 0.02 and upper cut-off mass ~ 1.3* 10^7^ M_{sun}_, is also in agreement with that of nearby disc galaxies. A trend is found in the mass spectrum index from steep to shallow as we move to inner radii. Although the GMCs are in an elliptical galaxy, the general GMC properties in the molecular disc are as in spiral galaxies. However, in the CND, large offsets in the line-width-size scaling relations (~0.3 dex higher than those in the GMCs in the molecular disc), a different XCO factor, and the shallowest GMC mass distribution shape ({gamma} = -1.1 +/- 0.2) all suggest that there the GMCs are most strongly affected by the presence of the active galactic nucleus and/or shear motions.