Constrained second-order convex optimization algorithms are the method of choice when a high accuracy solution to a problem is needed, due to their local quadratic convergence. These algorithms require the solution of a constrained quadratic subproblem at every iteration. We present the Second-Order Conditional Gradient Sliding (SOCGS) algorithm, which uses a projection-free algorithm to solve the constrained quadratic subproblems inexactly and uses inexact Hessian oracles (subject to an accuracy requirement). When the feasible region is a polytope the algorithm converges quadratically in primal gap after a finite number of linearly convergent iterations. Once in the quadratic regime the SOCGS algorithm requires \(\mathcal {O}(\log (\log 1/\varepsilon ))\) first-order and inexact Hessian oracle calls and \(\mathcal {O}(\log (1/\varepsilon ) \log (\log 1/\varepsilon ))\) linear minimization oracle calls to achieve an \(\varepsilon \) -optimal solution. This algorithm is useful when the feasible region can only be accessed efficiently through a linear optimization oracle, and computing first-order information of the function, although possible, is costly.