Adders are very important in Digital Signal Processing (DSP) for filter designing. It is profoundly accepted that the main processing unit of any device capable of carrying out computations is the Central Processing Unit (CPU). The most fundamental and integral part of the CPU is an Arithmetic and Logical Unit (ALU). Adders are the primary and indispensable component of ALU. There are various adders available in the literature such as Ripple Carry Adder (RCA), Carry Look Ahead Adder (CLA), Carry Skip Adder (CSA), and Carry Increment Adder (CIA), etc. In this paper, a new hybrid adder is designed by combining the two significant adders such as the Carry Skip adder and the Carry increment adder. The hybrid adder has two main peripheral components namely RCA and Multiplexer. In this paper, the GDI technique is applied in both RCA and Multiplexer to design a new low-powerhigh-speed hybrid adder. Simulation is done using the Tanner EDA tool in 180nm technology and the results obtained show a significant improvement in power consumption and delay.