Can't recall offhand where I have seen this very low crossbar. Probably German early 20th century.
Almost as low and with a similar style, Shango:
http://www.myfonts.com/fonts/castletype/shango/
Don

Thank you Don. May I ask you one more question? Do you know any that also have lower case? I would like to know how they work together with such low crossbar.

Will check some more for a low crossbar on A serif with a lower case.
Perhaps another typophile could make a suggestion.
This design is rare for serifed fonts but is found in some art deco sans. These tend to have a lot of exaggeration in letter shapes. For example Party At Gatsbys by T.W. Jeffery:

Ana - not knowing what, besides the low crossbar, you are after, I'll offer five options ...

The first is Windsor Light (or Light Condensed).

The next two are based on the early twentieth century lettering of Elizabeth Colwell. There is the fanciful McKenna Handletter and even quirkier Colwell.

Next there is Handle Old Style.

And last, with its mini-serifs, is Doug Olena's Elegant.

Mike's reference to Douglas F. Olena's Elegant led me to track down its availability at Linotype
Elegant Open Face
http://www.linotype.com/176897/elegantopenface-font.html
Elegant Inline
http://www.linotype.com/176894/ElegantInline-product.html
Serifs that are mirco -- smaller than mini!-- with one of the lowest crossbars on A that I have seen, and including a fairly conventional lower case.
Don

Hi Mike, like your suggestions. Any idea as to the person who created Handle Old Style? The reference to Monotype Design Studio is very general.
Don

Don - I don't know who created Handle Oldstyle. My copy has a copyright of 2003, Agfa Monotype. I'm nearly certain it was a Compugraphic property before that.

I wonder why Linotype doesn't offer the solid variant of Elegant.

Thank you Don and Mike for your help. :)

Hi Ana, you're welcome.
Hi Mike, so the creator remains a mystery. As for Linotype's font selection I note that they only offer a few of Doug Olena's fonts, even though most of his fonts are good quality designs not found elsewhere. Fortunately he sells them through his own website, Keystrokes.
Don