The detection of X-ray emission constitutes a reliable and efficient tool for the selection of Active Galactic Nuclei (AGNs), although it may be biased against the most heavily absorbed AGNs. Simple mid-IR broad-band selection criteria identify a large number of luminous and absorbed AGNs, yet again host contamination could lead to non-uniform and incomplete samples. Spectral Energy Distribution (SED) decomposition is able to decouple the emission from the AGN versus that from star-forming regions, revealing weaker AGN components. We aim to identify the obscured AGN population in the VIPERS survey in the CFHTLS W1 field through SED modelling. We construct SEDs for 6,860 sources and identify 160 AGNs at a high confidence level using a Bayesian approach. Using optical spectroscopy, we confirm the nature of ~85% of the AGNs. Our AGN sample is highly complete (~92%) compared to mid-IR colour selected AGNs, including a significant number of galaxy-dominated systems with lower luminosities. In addition to the lack of X-ray emission (80%), the SED fitting results suggest that the majority of the sources are obscured. We use a number of diagnostic criteria in the optical, infrared and X-ray regime to verify these results. Interestingly, only 35% of the most luminous mid-IR selected AGNs have X-ray counterparts suggesting strong absorption. Our work emphasizes the importance of using SED decomposition techniques to select a population of type II AGNs, which may remain undetected by either X-ray or IR colour surveys.