The IEEE 802.15.4 is a standard for Wireless Personal Area Network (PAN) that supports low data rate, low cost, low complexity and low power consumption applications. The CSMA/CA algorithm of the IEEE 802.15.4 MAC layer employs the Binary Exponential Backoff (BEB) function to compute the backoff delay for each node. Using BEB function, it is possible that two or more nodes may collide if they choose the same backoff exponent value. Consequently this will increase collision and network contention level which will degrade the network overall performance. To overcome this problem, this paper proposes a Fibonacci Backoff (FIB) function to compute the backoff interval. In FIB, each node shall wait for an incremental backoff periods as they need to access the channel. The performance of FIB algorithm is compared against the BEB function.