Natural invisibility
Would a real life invisibility suit be possible? Well, let's see.
In nature, some animals have camouflage. But that's not the same as invisibility. Camouflage is changing skin color because of adapting to the environment, but invisibility is complete transparency of every single part of your body. So actual invisibility is impossible, but there might be a way to cause an illusion of invisibility.
Already existing solution
Believe it or not, but there is already an existing invisibility cloak. It's called Quantum Stealth, and it works by bending light waves. However, it doesn't make you completely invisible. It looks like a dirty window, you can see trough it but you know something is there.
My solution
But i came up with something too. What if you have a suit covered in little screens and cameras which are all connected to each other, and the screens display what the cameras on the oppisite side of the suit are recording? You wouldn't be able to see the person in the suit, creating a fake kind of invisibility.