Time-series modeling of PV output for solar panels can help solar panel owners understand the power systems' time-varying behavior and be prepared for the load demand. The time-series forecast/prediction can become challenging due to many missing observations or a lack of historical records that are not sufficient to establish statistical models. Increasing PV measurement frequency over a longer period increases the cost in the detection of the PV fluctuation. This paper proposes an efficient approach to iterative multi-task learning for time series (MTL-GP-TS) that improves prediction of the PV output without increasing measurement efforts by sharing the information among PV data from multiple similar solar panels. The proposed iterative MTL-GP-TS model learns/imputes unobserved or missing values in a dataset of time series associated with the solar panel of interest to predict the PV trend. Additionally, the method improves and generalizes the traditional multi-task learning for Gaussian Process to the learning of both global trend and local irregular components in time series. A real-world case study demonstrated that the proposed method could result in substantial improvement of predictions over conventional approaches. The paper also discusses the selection of parameters and data sources when implementing the proposed algorithm.