The cross sections of state-selective charge exchange (CX) between highly charged ions and neutrals are important for modeling extreme ultraviolet and soft X-ray emissions in many astrophysical objects with hot plasma impacting cold media. By using cold-target recoil-ion momentum spectroscopy, we measure O6+ CX collisions with He and H2 in the collision energy range of 19.5 to 100 keV amu−1. The relative cross sections of state-selective single CX are reported for electron capture into O5+(1s
2
nl) n = 2, 3, 4, 5, ≥6 and n = 3, 4, 5, ≥6 for He and H2, respectively. With the collision energy increasing to 100 keV amu−1, the main capture channel shifts to higher n for both target species as compared to available theoretical results. We also report state-selective cross sections for double CX with He, where doubly excited states of
O
4
+
(
1
s
2
nln
′
l
′
)
with
nln
′
l
′
being 2s
2 (1S), 2s2p (1P), 2p
2 (1D), and 2p
2 (1S) [symmetric configurations] and 2s3l, 2p3l−2s4l, and 2s5l−2p5l [asymmetric configurations] are distinguished. It is found that the contributions of doubly excited states with asymmetric configurations are dominant and symmetric configurations increasingly come into play with the increase of collision energy. The present results provide experimental benchmarks available for theoretical calculations.