The Gaussian process (GP) latent variable model (GPLVM) has the capability of learning low-dimensional manifold from highly nonlinear data of high dimensionality. As an unsupervised dimensionality reduction (DR) algorithm, the GPLVM has been successfully applied in many areas. However, in its current setting, GPLVM is unable to use label information, which is available for many tasks; therefore, researchers proposed many kinds of extensions to the GPLVM in order to utilize extra information, among which the supervised GPLVM (SGPLVM) has shown better performance compared with other SGPLVM extensions. However, the SGPLVM suffers in its high computational complexity. Bearing in mind the issues of the complexity and the need of incorporating additionally available information, in this paper, we propose a novel SGPLVM, called supervised latent linear GPLVM (SLLGPLVM). Our approach is motivated by both SGPLVM and supervised probabilistic principal component analysis (SPPCA). The proposed SLLGPLVM can be viewed as an appropriate compromise between the SGPLVM and the SPPCA. Furthermore, it is also appropriate to interpret the SLLGPLVM as a semiparametric regression model for supervised DR by making use of the GP to model the unknown smooth link function. Complexity analysis and experiments show that the developed SLLGPLVM outperforms the SGPLVM not only in the computational complexity but also in its accuracy. We also compared the SLLGPLVM with two classical supervised classifiers, i.e., a GP classifier and a support vector machine, to illustrate the advantages of the proposed model.