A recruitment agency (X) called me, requiring me for a job in company (Y). I asked them (X) to make someone from (Y) to call me (X) told me that HR of (Y) will call me. No one in (Y) called me for a month. Can I Contact HR (Y) directly?

You can call the company’s HR to ask if they have any open positions and where to send a resume or fill out an application.

But you can’t call them about what the recruiter was talking about. The company may have no record or knowledge of your interest in whatever the recruiter was talking about. And if you call them about it, it puts them on the spot and they won’t like that.

No, you shouldn’t. The recruiter may not have ever informed the company about you, if you didn’t meet their standards or their screening.

I agree with @zenvelo and his approach.

Okay, but I want to tell you that the recruiter told me the name of HR, and I found that it is real. How can I be sure that the HR had my CV already or how to know HR’s plan? If I call him, he might asked me how I know that they want an employee.

It doesn’t matter that the recruiter told you that. If you call the HR person, you are never going to get the job, or any other job with that company, and the recruiter will never call you again.

Do you have any sort of contract with X? Have they done anything for you in the past, or do you have more of a relationship with them than this one interaction about Y? Have you heard from X or called X since they said Y would call you?

No, it’s the first deal for me from X.

Yes, X called me last week and asked me if Y had called me or not, and I said “Y didn’t call me.”

X said “okay, we will see and give you the updates,” but they did’t call me again.

I’d call X back when it’s been 4–5 business days since you last talked to them, and request an update.