The split feasibility problem (SFP) is finding a point in a given closed convex subset of a Hilbert space such that its image under a bounded linear operator belongs to a given closed convex subset of another Hilbert space. The CQ algorithm is one of the most popular iterative methods and relaxed CQ algorithm is used to solve the SFP where the two closed convex sets are both level sets of convex functions. The convergence of the relaxed CQ algorithm has been investigate in finie- or infinite-dimensional Hilbert spaces. We establish the linear convergence property for the dynamic stepsize relaxed CQ algorithm when using different kinds of stepsizes under the condition that the bounded error bound property for the SFP hold. Additionaly, we give some sufficient conditions for the validity of the error bound property.