Considering the eccentricity due to thermal deformation in helically coiled tube-in-tube heat exchanger installed on an aero-engine, flow and heat transfer in helical annulus under different eccentricity ratios (e) were numerically studied by using RNG k-epsilon turbulence model, in which the hot air flows in the annulus and the cold super-critical kerosene flows in the inner helical tube. The result shows that the flow field and heat transfer of the eccentric helical annulus are largely different from the concentric case. For positive eccentricity case, or e > 0 (meaning that the coil radius of the inner tube enlarges, or the annulus becomes wider at the inner side and narrowed at the outer side), the distribution of the local heat transfer coefficients on the annulus section transforms form the W-like curves in concentric case into the fluctuant curves. In such a case, the heat transfer at the inner side of the annulus enhances obviously due to the increased axial velocity, while at the outer side the heat transfer only decreases slightly due to the secondary flow at the outer side, so that the average heat transfer is enhanced under positive eccentricity, and when e = 30%, the Nusselt number Nu(a) has an increase of 10% compared with the concentric case. For negative eccentricity, e < 0 (the annulus becomes narrowed at the inner side and wider at the outer side), the W-like distribution of local heat transfer coefficients under concentric case turns into the V-like one. Correspondingly, the heat transfer at the inner side of the annulus is weakened by the reduced axial velocity, while the heat transfer at the outer side increases only slightly due to the minor increase in axial velocity and secondary flow intensity, so that the average heat transfer is decreased under negative eccentricity. In this case, the Nu(a) will reach to the minimum at e =-50% with a decrease of 13.8% in comparison to the concentric case. For the helically coiled tube-in-tube heat exchanger used in an aero-engine, the thermal deformation under working condition will produce a negative eccentricity, and therefore it should be designed in positive eccentric way to offset the side effect of the thermal deformation.