Quantum-dot Cellular Automata (QCA) is one of the rapidly growing nano-electronic computing technology. QCA is based on electron presents in quantum dots. QCA technology have features on high density, low power and smallest design compare to the other technologies. This paper proposed the basic paradigm of an efficient design of a 4-bit binary Logical Left Shifter circuit for single shift as well as multiple shifts. Due to inherent nature, QCA has been utilized in this paper to achieve low power faster circuit for proposed design. These shifter circuits are useful in floating point processing systems, particularly very useful for mantissa multiplication technique. All the designs are implemented with QCADesigner tool. The accuracy is verified comparing theoretical values and corresponding simulation results.