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The accurate estimation of photometric redshifts plays a crucial role in accomplishing science objectives of the large survey projects. The template-fitting and machine learning are the two main types of methods applied currently. Based on the training set obtained by cross-correlating the DESI Legacy Imaging Surveys DR9 galaxy catalogue and SDSS DR16 galaxy catalogue, the two kinds of methods are used and optimized, such as EAZY for template-fitting approach and CATBOOST for machine learning. Then the created models are tested by the cross-matched samples of the DESI Legacy Imaging SurveysDR9 galaxy catalogue with LAMOST DR7, GAMA DR3 and WiggleZ galaxy catalogues. Moreover three machine learning methods (CATBOOST, Multi-Layer Perceptron and Random Forest) are compared, CATBOOST shows its superiority for our case. By feature selection and optimization of model parameters, CATBOOST can obtain higher accuracy with optical and infrared photometric information, the best performance ($MSE=0.0032$, $\sigma_{NMAD}=0.0156$ and $O=0.88$ per cent) with $g \le 24.0$, $r \le 23.4$ and $z \le 22.5$ is achieved. But EAZY can provide more accurate photometric redshift estimation for high redshift galaxies, especially beyond the redhisft range of training sample. Finally, we finish the redshift estimation of all DESI DR9 galaxies with CATBOOST and EAZY, which will contribute to the further study of galaxies and their properties.