You might be able to lose weight by only walking, depending on the duration and intensity of your walking and what your diet's like. But eating fewer calories through dietary changes seems to promote weight loss more effectively than does physical activity.
That's not to say physical activity, such as walking, isn't important for weight control -- it is. If you add 30 minutes of brisk walking to your daily routine, you could burn about 150 more calories a day. (To lose a pound a week, you generally need to eliminate 500 calories a day.) Of course, the more you walk and the quicker your pace, the more calories you'll burn.
To reap the most health benefits from exercise, your exercise intensity must generally be at a moderate or vigorous level. For weight loss, the more intense your exercise, or the longer you exercise, the more calories you burn. However, balance is important. Overdoing it can increase your risk of soreness, injury and burnout. If you're new to regular exercise and physical activity, you may need to start out at a light intensity and gradually build up to a moderate or vigorous intensity.
Once you've lost weight, exercise is even more important -- it's what helps keep the weight off. In fact, studies show that people who maintain their weight loss over the long term get regular physical activity. So keep walking, but make sure you also follow a healthy diet.