In continual learning (CL), model growth enhances adaptability over new data, improving knowledge retention for more tasks. However, improper model growth can lead to severe degradation of previously learned knowledge, an issue we name as growth-induced forgetting (GIFt), especially in task-agnostic CL using entire grown model for inference. Existing works, despite adopting model growth and random initialization for better adaptability, often fail to recognize the presence of GIFt caused by improper model growth. This oversight limits comprehensive control of forgetting and hinders full utilization of model growth. We are the first in CL to identify this issue and conduct an in-depth study on root cause of GIFt, where layer expansion stands out among model growth strategies, widening layers without affecting model functionality. Yet, direct adoption of layer expansion presents challenges. It lacks data-driven control and initialization of expanded parameters to balance adaptability and knowledge retention. This paper presents a novel SparseGrow approach to overcome the issue of GIFt while enhancing adaptability over new data. SparseGrow employs data-driven sparse layer expansion to control efficient parameter usage during growth, reducing GIFt from excessive growth and functionality changes. It also combines sparse growth with on-data initialization at training late-stage to create partially 0-valued expansions that fit learned distribution, enhancing retention and adaptability. To further minimize forgetting, freezing is applied by calculating the sparse mask, allowing data-driven preservation of important parameters. Through experiments across datasets with various settings, cases and task numbers, we demonstrate the necessity of layer expansion and showcase the effectiveness of SparseGrow in overcoming GIFt, highlighting its adaptability and knowledge retention for incremental tasks.