\(L\)-statistics, a linear combination of order statistics, are important and used in practice. Theoretically, there are some good properties, such as robustness, etc. Up to now, most work on \(L\)-statistics has focused only on univariate data. In this paper, projection pursuit techniques are employed to develop a class of \(L\)-statistics for multivariate data, which is used to test a certain class of hypotheses. The main idea is to choose a univariate \(L\)- statistic as a projection index so that a class of multidimensional \(L\)- statistics can be established. The corresponding asymptotic null distributions of the test \(L\)-statistics are derived. As illustration, some applications to location and dispersion testing problems are considered.