Is there any grammatical mistake? "Learn to speak English in easy methods"?

I think you are right. There is something wrong with it. We don't say "Learn to speak English in easy methods." We know by the sound of it that it's wrong if we are native speakers. But why is it wrong? (We do say "methods," by the way.) "Learn to speak English" is good. But "in easy methods" is not. We can say "using easy methods." But it's still vague, if you are advertising something you have written in order to teach English, saying "With these easy methods" makes it good. My thought was "Learn to speak English using these easy methods." (I hope that you are going to learn or teach English with the aid of a native speaker. There's just too much subtlety and custom involved. If a person can't "hear" what's good English and what's not, they shouldn't be involved with teaching it.) Even native speakers use poor English all the time! Now, even your question:

"Is there any grammatical mistake?" isn't a complete sentence! It would have to be something like: "Is there any grammatical mistake in the following?" Or "Is there any grammatical mistake in this statement?" or just "Is there any grammatical mistake in this?" or EVEN "Is there any grammatical mistake in…? "Learn to speak English etc. "

end with "by this easy method"

methods is wrong, try steps.

I'd word it like "You can learn to speak English with these easy methods."