It is a very old building with plug fuse panels. one of the panel needs to be changed. I couldn't find a same panel, so I bought a breaker panel which is smaller in size than the original one. The question is how I should deal with the cables that has been peeled into the old panel? Can I just wrap electrical tape on them before they enter the new panel? or is there any other way to protect the wires outside panel?

I am not sure if your aware or not but to modify an electrical installation your need a permit.Even if you own the building.

I'm pretty sure that would not be allowed. For two reasons:

a) It would look horribly ugly and unprofessional which, in my opinion, does not count as neat workmanship.

b) Tape, even many layers, is not nessicarily suitable for protecting the conductors from clamps.

I can't imagine any inspector being happy with that installation.

I'm concerned based on the nature of your question, and the fact that you had to ask, that you're probably not skilled enough to perform this installation safely. A qualified person would've gone for an approach using some type of junction box.

Thank you for your replies. I will use a junction box, although the wires are just 1 or 2 inches shorter to the panel.