It's Hydrangea paniculata.

I concur with carol23. The panicle shaped blooms suggest that it is a paniculata. Climbing hydrangea (Hydrangea anomala ssp. petiolaris) has white lacecap blooms (see the link below for a picture). It prefers to climb up a "surface" (tree, fence, etc) or spread on the ground, as opposed to creating a bush like the one on the picture.

Paniculatas will develop white panicle-shaped large blooms in June but some like Tardiva may bloom much later. After 3-4 weeks, the white blooms will change color. They are very cold hardy and will tolerate growing in clayish soils (up to a point). While some dwarf versions are being introduced lately, most tend to be 8-10 feet tall or more. Grandiflora (also known as Pee Gee) will get even taller and can be grown as a tree. The large blooms can be a problem sometimes when they get wet, causing an arching shrub effect.

Some well known paniculatas: Burgundy Lace, Grandiflora, Kyushu, Limelight (Little Lime is the dwarf version), Pee Wee, Pink Diamond, Pinky Winky, Tardiva, Unique, Vanilla Strawberry, White Moth, etc

Close up of the blooms:
http://www.botanikfoto.com/en/details/image-photo-climbing-hydrangea-hydrangea-anomala-petiolaris-472397.php

Here is a link that might be useful: Picture of a climbing hydrangea in bloom

Like many other climbing shrubs climbing hydrangea forms a mound where a vertical support that would take it higher is not present. But, apart from other differences from H. paniculata its stems angle downward rather than up.