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A method for forecasting a nonequidistant (irregular) time series with an irregular sampling interval is presented. Data presented as irregular time series are often encountered in various fields, such as healthcare, biomechanics, economics, climatology, and others. Forecasting irregular time series is in demand in these fields for early warning and proactive decision-making, but there is no universal method for taking into account the unevenness of sampling in the forecast, which determines the relevance of research in this area. The purpose of the study was to develop a method for forecasting a nonequidistant series based on deep neural networks, which allows for good forecast accuracy with a relatively lightweight network architecture. The novelty of the research results lies in the developed method for forecasting nonequidistant time series, the architecture of the deep neural network, and the algorithm that implements the proposed forecast method. The method uses a closed loop, in which the forecast results at the current step are used at the following steps. The original feature of the proposed forecasting method is the use of a multilayer perceptron to forecast the duration of the next irregular sampling interval. This interval is calculated taking into account the correlation time calculated based on the autocovariance function of the durations of irregular sampling intervals. A distinctive feature of the proposed architecture is the presence of a separate input channel of neural network data for analyzing the values of sampling intervals, which allows forecasting the next value of the series taking into account the duration of the forecasted sampling interval. The method is developed for a one-dimensional series, but it can be extended to multidimensional series if the synchronicity of the sampling of the components of the series is observed. The computational experiments showed that with low requirements for computing resources, the accuracy of the forecast based on the proposed method is comparable to modern forecast models within the correlation interval.