The water injection is usually used as an oil recovery method due to its efficiency in recovering oil that is trapped in the reservoir. An injectivity test basically consists of continuously injecting a phase (water or gas), for a certain period of time, into an oil-saturated reservoir. From the analysis of the wellbore pressure behavior, this procedure aims to estimate, in addition to the volume of recoverable oil, parameters of the reservoir, such as permeability, film effect, among others. Nowadays, in the literature are found studies referring to a single injection period (and a single fall-off period) in multilayer reservoirs and studies referring to a single layer reservoirs considering variable injection flow-rates. In this context, this work aims to propose an approximate analytical solution for the pressure behavior in a multilayer reservoir considering a scheme of multiple flow-rates. The accuracy of the proposed solution was evaluated by comparison to a commercial finite difference-based flow simulator in different scenarios. The results express a considerable agreement between the data provided by the numerical simulator and the proposed model.