This study concerns solving semidefinite programming (SDP) problems using a new kernel-based primal-dual interior-point method (IPM). We propose a parameterized kernel function (KF) that has a hyperbolic barrier term. Taking advantage of the exponential convexity property of the new KF, we prove that the corresponding algorithm has a complexity of order O(√n log n log n/ε)  for large-update methods. To the best of our knowledge, this is the first hyperbolic KF for SDP to reach the best-known iteration bound for such methods. Preliminary numerical experiments indicate that the new KF is efficient compared with other existing KFs in the literature.