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I would like to use both in my sentence. However, I do not know whether I used it correctly or not.

Here is my sentence:

For both the bivariate and multivariate model, the new model shows a significant performance.

Is this correct? I think I cannot use the after both.

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Yes, you can use the after both. However, using both makes the first clause plural. The clause would need to end with multivariate models,. If you wanted it to remain singular, choosing either but not both, then you would use either instead of both. Since the second clause is definitely singular, either would be a better choice.

I hope you don't mind me going beyond your question. The sentence is a little awkward, repeating the noun 'model' in close proximity. It might sound slightly better as:

For either bivariate or multivarite, the new model ..., or even
Whether bivariate or multivarite, the new model ...

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