Does Reform Judaism recognize children of Jewish father as Jews (under conditions that father is Jewish both from mothers and fathers side). If so, that person does not have to go through conversion in order to marry Jewish girl?
In simple words, yes. According to Reform Judaism, the children of Jewish father is a Jew, even if the mother is not, as long as the child was brought up with an exclusively Jewish background. See also Wikipedia and Jewish Virtual Library.
So a person born with only one Jewish parent, whether it is the father or the mother, is considered fully Jewish according to Reform Judaism, and is entitled to all the privileges thereof. This means he would be allowed to marry another Reform Jewish girl and become a member of a Reform synagogue.
It must be noted, however, that both Conservative and Orthodox Judaism only consider someone a Jew if their mother is Jewish, regardless the status of the father. A person born of a non-Jewish mother is considered fully Gentile, regardless of whether his father was Jewish or not, according to Conservative and Orthodox Judaism. This means that such a person would not be allowed to marry a Jewish girl or become a member in a synagogue within Orthodox and Conservative circles.
Please see: https://en.wikipedia.org/wiki/Who_is_a_Jew%3F