A numerical model based on the Transfer matrix method (TMM) is proposed for the first time to study the gold coated tapered fibre optic surface plasmon resonance (SPR) with eight different types of taper profiles namely linear, exponential-linear, Gaussian, quadratic, sinusoidal, error function type and highly perturbed taper profile so-called chirp type of profile. The performance in terms of sensitivity, full width at half maximum (FWHM), detection accuracy (D.A.), amplitude dip, and half power points are estimated with respect to tapering ratio and choices of taper profile. It is found that sensitivity increased almost linearly with the taper ratio of each taper choice for the account of the reduction of detection accuracy. It has been found that sensitivity is highest for the case of chirp taper profile and lowest for the case of quadratic taper profile at low taper ratio. In this study, the aqueous solution is considered for sensor development which is adulterated by biomolecules species like DNA, blood samples, etc.