My basement bathroom in the shower drain I feel air coming through and when it rain I can time can hear the water running noise. (Recently I bought this house.)

My question is
Is it possible the drainer missing a trap.
It is OK to keep as it is or I need to do a repair ( no bad smell coming)

Pour some water down the pipe and see if it stops the water noises that you hear. If it does you will have to put water in that pipe on occasions to keep water in the trap.

Let me add a bit to Letmetellu's answer. Shine a light down the drain. Do you see water? Put a stick down the drain. Is the stick wet for 3 or 4 inches?
If the answer's no to any of these then you are not trapped and you have a direct connection between your shower drain and the sewer allowing sewer gas to enter your home. Sewer gas is harmful to your familys health and the methane content makes the gas explosive. Have it looked at at once. Good luck, Tom