Bluetooth is a common wireless technology that is widely used as a connection medium between various consumer electronic devices. The receivers mostly adopt the Viterbi algorithm to improve a bit error rate performance but are hampered by heavy hardware complexity and computational load due to a coherent detection and searching for the unknown modulation index. To address these challenges, a non-coherent maximum likelihood estimation detector with an eight-state Viterbi is proposed for Gaussian frequency-shift keying symbol detection against an irrational modulation index, without any knowledge of prior information or assumptions. The simulation results showed an improvement in the performance compared to other ideal approaches.