Long term memory (LTM) in climate variability is studied by means of fractional integral techniques. By using a recently developed model, Fractional Integral Statistical Model (FISM), we in this report proposed a new method, with which one can estimate the long-lasting influences of historical climate states on the present time quantitatively, and further extract the influence as climate memory signals. To show the usability of this method, two examples, the Northern Hemisphere monthly Temperature Anomalies (NHTA) and the Pacific Decadal Oscillation index (PDO), are analyzed in this study. We find the climate memory signals indeed can be extracted and the whole variations can be further decomposed into two parts: the cumulative climate memory (CCM) and the weather-scale excitation (WSE). The stronger LTM is, the larger proportion the climate memory signals will account for in the whole variations. With the climate memory signals extracted, one can at least determine on what basis the considered time series will continue to change. Therefore, this report provides a new perspective on climate prediction.