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Anderson(<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>m</mi><mn>0</mn></msub></mrow></semantics></math></inline-formula>) extrapolation, an accelerator to a fixed-point iteration, stores <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>m</mi><mn>0</mn></msub><mo>+</mo><mn>1</mn></mrow></semantics></math></inline-formula> prior evaluations of the fixed-point iteration and computes a linear combination of those evaluations as a new iteration. The computational cost of the Anderson(<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>m</mi><mn>0</mn></msub></mrow></semantics></math></inline-formula>) acceleration becomes expensive with the parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>m</mi><mn>0</mn></msub></mrow></semantics></math></inline-formula> increasing, thus <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>m</mi><mn>0</mn></msub></mrow></semantics></math></inline-formula> is a common choice in most practice. In this paper, with the aim of improving the computations of PageRank problems, a new method was developed by applying Anderson(1) extrapolation at periodic intervals within the Arnoldi-Inout method. The new method is called the AIOA method. Convergence analysis of the AIOA method is discussed in detail. Numerical results on several PageRank problems are presented to illustrate the effectiveness of our proposed method.