I am currently a PhD student. I have a previous publications on my field in a top tier conference. Now my adviser wants to extend the work. The problem is when I started working on that again, I found some results were not correct in the published paper. I did mistakes unintentionally interpreting the results previously, but somehow the reviewer did not notice that. Now I am too worried telling about this to my adviser. Can you please suggest me how to approach this to my adviser? What can be the consequence of this to the published paper?
One way or the other, you will have to build a relationship with your adviser in which you can discuss such questions. In this regard, your relationship with your adviser is no different than with your wife or girlfriend: waiting too long doesn't make the problem go away.
This might just be the right time to start talking about difficult issues.
Unfortunately there are no two ways about it. Mistakes can and do happen. It is better to go forward with it to your adviser than try to tip-toe around/through it. Ostensibly, your adviser is on your side. If there really was a mistake perhaps both of you can try to understand what went wrong. Perhaps there is a way to redo your analysis or solve the issue you are having.
The consequence to the published paper might be that it is retracted. This will depend, was it a conference paper or a journal article? I think it is unfortunate that a lot of people look down on being wrong. Obviously the goal is to be right more often than not. But letting known false findings linger can only harm your career and field. And you don't want to get into a scenario where someone else finds it and then your honest mistake comes into question as being nefarious.
I suggest that you approach your adviser in a one-on-one meeting and clearly explain your old findings and how you got them, compared to your new findings and how you realized there was an error. Suggest that perhaps both of you can look into fixing the error some how. Or if not ask them to suggest how to approach dealing with the mistake.
If the paper is on your website upload a corrected version with a note about the mistake. If this was published in an academic journal you are going to have to contact them most likely as well. They may decide to publish a note or retraction. Its best to be open and honest about what happened, as you say it was a mistake. So you have nothing to hide. Hope this helps! Good Luck.