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Today I've read interesting fact and actually have no idea to create a homomorphism between two objects.

Consider a twice retorted strip and side surface of cylinder. Then they are homeomorphic.

Any idea of bijection ?

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    Forget the problem for a moment, and try parametrizing both. Then go back to the problem. (incidentally, I don't know what "skewed on 360°" might mean) – 2017-02-26
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    @Hurkyl make some edition. – 2017-02-26
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    So what is a twice retorted strip? – 2017-02-26
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    Try to show that the open cylinder $[0,1] \times (0,1)$ is homeomorphic to the open "twisted" by 180° band. Do it twice and glue them together. – 2017-02-26
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    @HaraldHanche-Olsen sorry for my English.I mean consider band , which twice twisted (twist from the both side by 180 degree). – 2017-02-26
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    Okay, so you can parametrize it by a map $[0,2\pi]\times[-1,1]$ so that $(\theta,t)\mapsto\bigl((2+t\cos\theta)\cos\theta,(2+t\cos\theta)\sin\theta,t\sin\theta\bigr)$, if I'm not misunderstanding. That ought to help. – 2017-02-26
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    And right side of bijection is my band ? – 2017-02-26

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Unlike Mobius band which twist a half, the band in your question twist 360 degree. The homeomorphism is this: cut the band, twist the resulted strip 360 degree and paste the cut points again. This is possible since you paste the cut points in the original direction, a method which can't be done for Mobius band. This is a obvious question in topology eccept if you want to think of topology as rubber-sheet geometry!