Yes it's normal. My first trimester I felt like I was starving all the time, even if I had just eaten. You're never supposed to 'eat for two' during pregnancy but starting the second trimester you're supposed to consume about 400 extra calories a day, which isn't really that much, depending on what you eat. Try eating healthy, a lot of fruits and veggies, drink a lot of water and eat high fiber foods. It's perfectly fine to indulge on something you're craving just don't go overboard. Just be careful to watch your weight. A lot of women use being pregnant as an excuse to let themselves go but that's not healthy for you or the baby.
Try changing what you eat if you are worried. The need to "snack" more often is normal in first trimester it does wonders for nausea but technically the eating fir two doesn't start till second trimester. It's all about quality not quantity, something I've struggled with for weeks (12&2) try fruits and grains things that will help you feel full longer and are healthy for you. But be glad your hungry more, some women get too much morning sickness to feel hungry in the early months!