ABSTRACT We first present new Subaru narrow-band observations of the Ly α halo around the quasi-stellar object (QSO) CFHQ J232908−030158 at z = 6.42, which appears the most luminous and extended halo at z > 5 (LLy α = 9.8 × 1043 erg s−1 within 37 pkpc diameter). Then, combining these measurements with available data in the literature, we find two different evolutions of QSOs’ Ly α haloes. First is a possible short-term evolution with QSO age seen in four z > 6 QSOs. We find the anticorrelation between the Ly α halo scales with QSOs’ infrared (IR) luminosity, with J2329−0301’s halo being the brightest and largest. It indicates that ionizing photons escape more easily out to circum-galactic regions when host galaxies are less dusty. We also find a positive correlation between IR luminosity and black hole mass (MBH). Given MBH as an indicator of QSO age, we propose a hypothesis that a large Ly α halo mainly exists around QSOs in the young phase of their activity due to a small amount of dust. The second is an evolution with cosmic time seen over z ∼ 2–5. We find the increase of surface brightness towards lower redshift with a similar growth rate to that of dark matter haloes (DHs) that evolve to MDH = 1012–1013 M⊙ at z = 2. The extent of Ly α haloes is also found to increase at a rate scaling with the virial radius of growing DHs, $r_\text{vir} ∝ M_\text{DH}^{1/3}(1+z)^{-1}$. These increases are consistent with a scenario that the circum-galactic medium around QSOs evolves in mass and size keeping pace with hosting DHs.