When reading a book about Algorithms, I meet one sentence:

We will demonstrate how to perform this type of running-time analysis to recursive algorithms.

Here is my question:

  • this type should be the object of verb perform according to position relationship. But I think perform analysis is more reasonable according to the meaning. So which comprehension is right ?

You are correct in inferring that what is performed is an analysis, not a type.

But the construction is not misleading. A type of X, or a kind, sort, variety, category of X does not denote something different from X; it denotes a subset of the class X. That is, there are presumably many analyses which may be described as 'running-time analyses'; when the authors write that they will "demonstrate how to perform this type of running-time analysis" they are understood to mean that they will demonstrate how to perform the running-time analyses which belong to this type—the type which has previously been described.

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