Asthma is a common disease. The clinical diagnosis is usually confirmed on a pulmonary function test, which is not always readily accessible. We aimed to develop a computationally lightweight handcrafted machine learning model for asthma detection based on cough sounds recorded using mobile phones. Toward this aim, we proposed a novel feature extractor based on a one-dimensional version of the published attractive-and-repulsive center-symmetric local binary pattern (1D-ARCSLBP), which we tested on a new cough sound dataset. We prospectively recorded cough sounds from 511 asthmatics and 815 non-asthmatic subjects (comprising mostly healthy volunteers), which yielded 1875 one-second cough sound segments for analysis. Our model comprised four steps: (i) preprocessing, in which speech signals and stop times (silent zones between coughs) were removed, leaving behind analyzable cough sound segments; (ii) feature extraction, in which tunable q-factor wavelet transformation was used to perform multilevel signal decomposition into wavelet subbands, allowing 1D-ARCSLBP to extract local low- and high-level features; (iii) feature selection, in which neighborhood component analysis was used to select the most discriminative features; and (iv) classification, in which a standard shallow cubic support vector machine was deployed to calculate binary classification results (asthma versus non-asthma) using tenfold and leave-one-subject-out cross-validations. Our model attained 98.24% and 96.91% accuracy rates with tenfold and leave-one-subject-out cross-validation strategies, respectively, and obtained a low-time complexity. The excellent results confirmed the feature extraction capability of 1D-ARCSLBP and the feasibility of the model being developed into a real-world application for asthma screening.