Bored with his isolated and monotonous life, an apathetic psychologist decides to intentionally go crazy by killing someone at random, believing that if the guilt doesn’t make him go crazy, the asylum to where he will be sent for having no reason for his cruel act will.

I like the goal, I like the idea.

Hello, there is a very good movie vaguely related to his idea: Edmond
http://www.imdb.com/title/tt0443496/?ref_=nm_flmg_act_38

I think that the final part of the logline could be cut ("believing that if the guilt doesn't make him go crazy, the asylum to where he will be sent for having no reason for his cruel act will"), because it's explanation instead of plot.

You could also find a precise inciting event that put the story in motion (be bored is a bit vague)... Can you think of a visuel event that can make the character realize how bored he is? Maybe his mother dies and he feels nothing (like in "the stranger" by Camus that you should read to get inspiration).

Then you need to find a clear source of conflict... what force opposes to his plan? He's bored, he stabs to death the first person on the street, end of the story?

Find an inciting event, find a source of conflict and you'll have a very good logline!

This concept seams bizarre and bizarre can be good but in my mind? in this instance it doesn't work as a concept because the bizarre element is un motivated.
Why does he suddenly decide to "...go crazy..."? If he is a psychologist would he not know that there is more to "going crazy" than just doing something bad? By any other standard the act of pursuing his own insanity is in itself insane so wouldn't he have achieved his goal before killing someone?

In addition I find it hard to believe that an audience would empathize with a MC who kills a person in order to go crazy himself.

About the logline here is no inciting incident and the goal, of going crazy, appears open ended because a question arises, what will he do after he goes crazy?

The second half of the sentence: "...believing that if the guilt doesn't make him go crazy, the asylum to where he will be sent for having no reason for his cruel act will..." doesn't describe a plot rather it is an explanation of the MC motivation and should either be significantly reduced or cut all together. If the MC's motivation isn't clear from the combination of the inciting incident and goal then an explanation needs to be brief and clear this one isn't.

Hope this helps.