The concepts of Bernoulli numbers B n , Bernoulli polynomials B n ( x ) , and the generalized Bernoulli numbers B n ( a , b ) are generalized to the one B n ( x ; a , b , c ) which is called the generalized Bernoulli polynomials depending on three positive real parameters. Numerous properties of these polynomials and some relationships between B n , B n ( x ) , B n ( a , b ) , and B n ( x ; a , b , c ) are established.