One challenge in applying bioinformatic tools to clinical or biological data is high number of features that might be provided to the learning algorithm without any prior knowledge on which ones should be used. In such applications, the number of features can drastically exceed the number of training instances which is often limited by the number of available samples for the study. The Lasso is one of many regularization methods that have been developed to prevent overfitting and improve prediction performance in high-dimensional settings. In this paper, we propose a novel algorithm for feature selection based on the Lasso and our hypothesis is that defining a scoring scheme that measures the "quality" of each feature can provide a more robust feature selection method. Our approach is to generate several samples from the training data by bootstrapping, determine the best relevance-ordering of the features for each sample, and finally combine these relevance-orderings to select highly relevant features. In addition to the theoretical analysis of our feature scoring scheme, we provided empirical evaluations on six real datasets from different fields to confirm the superiority of our method in exploratory data analysis and prediction performance. For example, we applied FeaLect, our feature scoring algorithm, to a lymphoma dataset, and according to a human expert, our method led to selecting more meaningful features than those commonly used in the clinics. This case study built a basis for discovering interesting new criteria for lymphoma diagnosis. Furthermore, to facilitate the use of our algorithm in other applications, the source code that implements our algorithm was released as FeaLect, a documented R package in CRAN.