What to do if the PM of the project you are working on is not competent?

It is a matter of making him feel like you are there to help him. You will need to "chat" with him regularly. You need him to feel that you are on "his side". Offer to take on small tasks. "I can help you updated that document". Then start making suggestions, like "what if we did it this way". Always use "we". Never point out a problem without having a potential solution. "I am worried about X missing the deadline, do you think we should do Y the help?'. Give him the information and guide him to make the decision.
It takes a lot of tact and letting go of your ego.

Hi Sergio,

I guess results are the most accurate way to measure it. I agree with Dinah and her comment is really useful. Probably he is really good in traditional PM, but when you change from traditional Project Management to Agile, things are not as easy as everybody guess. That's why I'm now in charge to support him, the thing is that it is my first time as a mentor and that's why I need lessons learned instead questions such as: "who are you to say he is not competent?" Those comments are a waste of time in my opinion. I'm asking support to manage this situation as best as possible, not to answer who I am to think something about somebody.

@Jesus, your comment about "traditional" vs "agile" shocked me..from my point of view there isn't any difference when you mentor/train or try to engage someone.

However, does it mean that you are trying to teach, help or engage him to be "more agile" ? Did someone informed him (Example his or your manager) that he need to learn and you will be supporting him?

The problem is named things like something project management. Project management is one and only one related to the way the organization decide to follow: PMI, GPM, IPMA, anything else. With that on hand then you can use different practices (Lean, Agile, etc) that sometimes determines the techniques and tools you will use. What you stated about competence is nothing to be with the practice you use. The worst thing you can do is to think that somebody is incompetent or somethig other thing. In fact, you can think that for yourselfe. But, it the organization put that person in that role is for a reason. And most of the time you do not have all the information about the reason.

Hi Mayte,

Well what usually happens when a new PM is joined to the team, a PM with experience in the organization is designed to mentor the new one. In this case, I guess it was mostly about the availability of PMs to mentor. I think different than you, traditional and agile approach is not the same and a traditional PM has to be guided. I have lead projects in both ways and there are some particularities to be considered to succeed. Of course, the manager exposed that.

Jesus,

If the manager already clarify the roles, then you have a big challenge to engage the team member!

On the other hand maybe you misunderstood me, I wasn't writing about how we lead or coordinate projects...from my point of view how to engage, convince, train, coach or mentor a team member isn't linked to the background you could be an amazing mentor in a manufacturing plant with lean six sigma and also managing a SAP implementation in a public department... From my point of view, be a mentor has more implications that teach someone something.