How to overcome current drop in circuit with high inductance value?
How can I make the current stay stable even when I switch the switch?


Try removing the diode across the current source. 

If you need the diode then please don't expect miracles with inductors - they fight against a changing current and, when the switch is activated, the inductor current will have fallen to zero amps thus, when opening the switch (to allow current to try and pass through the inductor) you can't expect all the 100 amps to instantly pass through it - the inductor will resist and that is what you see.

This is a fundamental property of inductor - they produce a counter emf proportional to the rate of change of current. This means if you expect an infinitely fast change in current, the inductor produces an infinitely high back emf to counter that change.