Vision-based　intelligent　systems　like　automatic　driving　or　driving　assistance　can　be　improved　by　enhancing　the　visibility　of　the　scenes　captured　in　bad　weather　conditions.　In　particular,　many　image　dehazing　algorithms　(DHAs)　have　been　proposed　to　facilitate　such　applications　in　hazy　weather.　Contrary　to　the　substantial　progress　of　DHA　developing,　the　quality　evaluation　of　DHAs　falls　behind.　Generally,　DHAs　can　be　evaluated　qualitatively　by　human　subjects　or　quantitatively　by　objective　quality　measures.　Compared　with　the　subjective　evaluation　which　is　time　consuming　and　difficult　to　apply,　objective　measures　with　quantitative　results　are　more　needed　in　practical　systems.　But　in　the　literature,　very　few　measures　are　widely　utilized,　and　even　less　measures　correlate　well　with　the　overall　dehazing　quality　(DHQ).　In　this　paper,　we　study　the　DHQ　evaluation　using　real　hazy　images　systematically.　We　first　construct　a　DHQ　database,　which　is　the　largest　of　its　kind　so　far　and　includes　1750　dehazed　images　generated　from　250　real　hazy　images　of　various　haze　densities　using　seven　representative　DHAs.　A　subjective　quality　evaluation　study　is　subsequently　conducted　on　the　DHQ　database.　Then,　we　propose　an　objective　DHQ　index　(DHQI)　by　extracting　and　fusing　three　groups　of　features,　including:　1)　haze-removing　features;　2)　structure-preserving　features;　and　3)　over-enhancement　features,　which　have　captured　the　most　key　aspects　of　dehazing.　DHQI　can　be　utilized　to　evaluate　DHAs　or　optimize　practical　dehazing　systems.　Validations　on　the　constructed　DHQ　database　and　three　other　databases　with　synthetic　haze　have　verified　the　effectiveness　of　DHQI.　Finally,　we　give　an　overview　of　the　current　DHA　quality　evaluation　strategies,　discuss　their　merits　and　demerits,　and　give　some　suggestions　on　systematic　DHA　quality　evaluation.　The　DHQ　database　and　the　code　of　DHQI　will　be　released　to　facilitate　further　research.