This paper presents a linear SVM (Support Vector Machine) Pyramidal Tree (SVMPT) for binary classification tasks. SVMPT is a modified version of SVM based Tree Type Neural Networks (SVMTNN), reported earlier in the literature . Both the algorithms use parameter-less SVM proposed by Mangasarian  for learning in each node. While SVMTNN insists on 100 percent training accuracy, linear SVMPT uses predetermined threshold value to determine when to stop adding new nodes. Experimental results on standard binary datasets show that the algorithm has good generalization capability, comparable to linear SVMs. We also present experimental results on extensions of linear SVMPT to multiclass datasets and datasets with fuzzy membership for each datapoint. © 2010 IEEE.