The Graceful Labelling of Trees is one of the most challenging Conjectures in Graph Theory, proudly known as the Disease of Graphtheory which still remains a challenge as it still remains unsolved. To counter the Conjecture, an algorithm is proposed to construct a Graceful Binary tree and a Graceful Caterpillar Tree. Here, the algorithm puts forward a solution to graceful Labelling problem through a very efficient and simple approach. Most importantl the Binary Tree exhibits the property of Gracefulness and the construction of the Tree remains one of the major contributions of the paper. The steps regarding the Algorithm are discussed and the other variants of the already known Graceful graphs are discussed. Here, a basic initiative to prove the Conjecture for Binary Trees as well as proposed version of Binary Cascading caterpillar are put forward. The result is known that all graphs are Graceful, but no algorithm of graceful labelling of graphs has yet been proposed. In this paper, we are proposing a simple method of graceful labelling Binary Cascading Caterpillar Trees and Complete Binary Graphs.