<p>A parareal-in-time algorithm is proposed and analyzed for solving a class of optimal control problems governed by ODE systems. These problems arise from the spatial semi-discretization of optimal control problems for distributed parameter systems or optimal controls of lumped parameter systems. The method addresses the first-order optimality system, which can be formulated as a two-point boundary value problem in time, using a time-domain decomposition technique. The parareal-in-time iterative algorithm comprises two components: a local parallel component and a global correction component. The local parallel component involves solving a family of subproblems on a fine time mesh, which can be efficiently handled in parallel. In contrast, the global correction component is solved on a coarse time mesh with low computational cost. We establish a convergence rate of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(O(\tau ^k)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>O</mi> <mo stretchy="false">(</mo> <msup> <mi>τ</mi> <mi>k</mi> </msup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> for the <i>k</i>-th iteration, where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\tau \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>τ</mi> </math></EquationSource> </InlineEquation> denotes the time step size. This rate is comparable to that of the standard parareal algorithm for initial value problems. The proposed method can also be extended to handle optimal control problems with pointwise control constraints or nonlinear governing equations, leading to a (semi-smooth) Newton-parareal algorithm. Several numerical examples are provided to support the theoretical convergence results.</p>