First, locate the category grid template. If you know for sure, which template is used, you can do that using the template path hints ( https://stackoverflow.com/questions/24273443/in-magento-1-9-0-0-how-can-i-enable-template-path-hint ).
Next, find how the image display is made. Be attentive, as this template type usually has two ways of product output methods: Grid and List. It's possible to make a mistake by editing the List, that, as a rule, goes first in the code.
In the standard theme, right after the check goes:
goes the List View block. In 'else' of this check goes the Grid View. This is the place, where the changes should be made. Find somewhat like this:
<img src="helper('catalog/image')->init($_product, 'small_image')->resize(135); ?>"
alt="stripTags($this->getImageLabel($_product, 'small_image'), null, true) ?>"
And change all the values for resize(), width and height with the values you need.