I found this spider in my house:

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<img src="http://luigitec.com/image/spider.jpg">

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Is this a banana spider? I'm ready to kill it if is poisonus...

Can't see the picture.

Sorry:
Correct link:
http://cecati19.edu.mx/imagen/spider.jpg
http://cecati19.edu.mx/imagen/spider.jpg

Is this a banana spider? I'm ready to kill it if is poisonus...

Yes, that looks like a North American golden orb weaver, often called a Banana spider. I prefer the more correct but longer name so as not to confuse it with the Brazilian wandering spider.

The North American golden orb weaver is relatively harmless, although it does have a venom. All spiders do. This species' is so dilute as to pose very little risk to humans.

Thanks!