The box in the ceiling has white, black, red, and ground.

Light Fixture has White, Black, and Green wire.

I have connected white to white, and green to ground.

If I connect black to black, the light turns on and won't shut off

If I connect black to red, then the light fixture doesn't work.

Please advice what I should do.

Can I connect black to both black & red together ?

If you have a red wire in the ceiling box there is a strong suggestion there is a second switch somewhere, a 3 way. Does you sitch say ON and OFF on the lever or is it blank? Do you have a test meter or a test light?

If you have a red wire in the ceiling box there is a strong suggestion there is a second switch somewhere, a 3 way.I don't think this is true at all. It simply suggests there is a constant feed and the red is a switch leg.
Now two reds in a box is a different story.

The simplest thing to do is pull the switch and tell us what wires are connected there.

Sounds like someone may have an unorthodox switch loop circuit. Normally, a black and a red would indicate a 3 way or 2 switched wires i.e. light and fan. Yes, pull the switch and load a picture or tell us what is there.

How To Install a 3-way Switch Option #8 :: Home Improvement Web (http://www.homeimprovementweb.com/information/how-to/three-way-switch-option8.htm) There are many ways to wire a 3 way and most home owners do not know how to do it so I never assume that home wiring is correct. I just worked on a dishwasher where the owner did not seem to know the difference between ground and neutral, it was a shocking experience

How To Install a 3-way Switch Option #8 :: Home Improvement Web (http://www.homeimprovementweb.com/information/how-to/three-way-switch-option8.htm) There are many ways to wire a 3 way and most home owners do not know how to do it so I never assume that home wiring is correct. I just worked on a dishwasher where the owner did not seem to know the difference between ground and neutral, it was a shocking experienceJust so you know, the diagram in this link is not only highly unorthodox and not at all used by anyone who knows what they are doing, it also is non-complaint to one of the most basic codes. Keeping all conductors of a circuit in the same raceway or cable.

Like I said, two reds in the ceiling certainly can be an indication of a 3-way, but it would be pretty rare. And the illegal example shown would be even rarer.