Automatic font image synthesis has been an extremely active topic in recent years. Various deep learning-based approaches have been proposed to tackle this font synthesis task by considering it as an image-to-image translation problem in a supervised setting. However, all such approaches mainly focus on one-to-one font mapping, i.e., synthesizing a single font style, making it difficult to handle more practical problems such as the font family synthesis, which is a one-to-many mapping problem. Moreover, this font family synthesis is more challenging because it is an unsupervised image-to-image translation problem, i.e., no paired dataset is available during training. To address this font family synthesis problem, we propose a method that utilizes a single generator to conditionally produce various font family styles to form a font family. To the best of our knowledge, our proposed method is the first to synthesize a font family (multiple font styles belonging to a font), instead of synthesizing a single font style. More specifically, our method is trained to learn a font family by conditioning on various styles, e.g., normal, bold, italic, bold-italic, etc. After training, given an unobserved single font style (normal style font as an input), our method can successfully synthesize the remaining styles (e.g., bold, italic, bold-italic, etc.) to complete the font family. Qualitative and quantitative experiments were conducted to demonstrate the effectiveness of our proposed method.