Experiments based on free space platform have demonstrated that the weak value amplification (WVA) technique can provide high sensitivity and precision for optical metrology. To promote this technique for real-world applications, it is more suitable to implement WVA based on optical fiber platform due to the lower cost, smaller scale and higher stability. In contrast to the free space platform, the birefringence in optical fiber is strong enough to cause polarization cross talk, and the amplitude-type noise must be taken into account. In theory, we deduct that the effect of amplitude-type noise will form noise ripples on the detection spectrum and can significantly compromise the sensitivity of WVA. To overcome this problem, a post-processing method is proposed and simulation results show the effectiveness of the method. Our results indicate the feasibility of implementing WVA based on optical fiber, which provide a possible way for designing optical sensors withhigher sensitivity and stability in the future.