It has been generally accepted that hyperspectral remote sensing is more effective and provides greater accuracy than multispectral remote sensing in many application fields. EO-1 Hyperion, a representative hyperspectral sensor, has much more spectral bands, while Landsat data has much wider image scene and longer continuous space-based record of Earth's land. This study aims to develop a new method, Pseudo-Hyperspectral Image Synthesis Algorithm (PHISA), to transform Landsat imagery into pseudo hyperspectral imagery using the correlation between Landsat and EO-1 Hyperion data. At first Hyperion scene was precisely pre-processed and co-registered to Landsat scene, and both data were corrected for atmospheric effects. Bayesian model averaging method (BMA) was applied to select the best model from a class of several possible models. Subsequently, this best model is utilized to calculate pseudo-hyperspectral data by R programming. Based on the selection results by BMA, we transform Landsat imagery into 155 bands of pseudo-hyperspectral imagery. Most models have multiple R-squared values higher than 90%, which assures high accuracy of the models. There are no significant differences visually between the pseudo- and original data. Most bands have Pearson's coefficients > 0.95, and only a small fraction has the coefficients < 0.93 like outliers in the data sets. In a similar manner, most Root Mean Square Error values are considerably low, smaller than 0.014. These observations strongly support that the proposed PHISA is valid for transforming Landsat data into pseudo-hyperspectral data from the outlook of statistics.