This paper proposes an adjustable and distributionally robust chance-constrained (ADRCC) optimal power flow (OPF) model for economic dispatch considering wind power forecasting uncertainty. The proposed ADRCC-OPF model is distributionally robust because the uncertainties of the wind power forecasting are represented only by their first- and second-order moments instead of a specific distribution assumption. The proposed model is adjustable because it is formulated as a second-order cone programming (SOCP) model with an adjustable coefficient. This coefficient can control the robustness of the chance constraints, which may be set up for the Gaussian distribution, symmetrically distributional robustness, or distributionally robust cases considering wind forecasting uncertainty. The conservativeness of the ADRCC-OPF model is analyzed and compared with the actual distribution data of wind forecasting error. The system operators can choose an appropriate adjustable coefficient to tradeoff between the economics and system security.