Acute Lymphocytic Leukemia is a type of cancer that occurs when abnormal white blood cells are produced in the bone marrow which do not function properly, crowding out healthy cells and weakening the immunity of the body and thus its ability to resist infections. It spreads quickly in children’s bodies, and if not treated promptly it may lead to death. The manual detection of this disease is a tedious and slow task. Machine learning and deep learning techniques are faster than manual detection and more accurate. In this paper, a deep feature selection-based approach ResRandSVM is proposed for the detection of Acute Lymphocytic Leukemia in blood smear images. The proposed approach uses seven deep-learning models: ResNet152, VGG16, DenseNet121, MobileNetV2, InceptionV3, EfficientNetB0 and ResNet50 for deep feature extraction from blood smear images. After that, three feature selection methods are used to extract valuable and important features: analysis of variance (ANOVA), principal component analysis (PCA), and Random Forest. Then the selected feature map is fed to four different classifiers, Adaboost, Support Vector Machine, Artificial Neural Network and Naïve Bayes models, to classify the images into leukemia and normal images. The model performs best with a combination of ResNet50 as a feature extractor, Random Forest as feature selection and Support Vector Machine as a classifier with an accuracy of 0.900, precision of 0.902, recall of 0.957 and F1-score of 0.929.