1. Make sure you’re singing in a suitable range.
All singers struggle more at the limits of their range, and if you haven’t had voice lessons before, you might well be picking notes which aren’t in your comfortable range.
One way to find a good note is to simple talk in your normal relaxed speaking voice. Then try talking in a “monotone” (i.e. not adjusting your pitch up and down for emphasis). Then try singing that note you were speaking. With this note which just “comes out naturally” you may well find it easier to maintain a steady pitch.
2. Try changing your volume.
The volume you sing with can greatly affect how easily you can keep a steady tone. If you’re singing quietly, you may find that singing louder makes it easier to hold a steady pitch. On the other hand, if you’re pushing your voice to be too loud, that can put strain on it, and if you sing a bit quieter you may find the pitch control easier.
Experiment with a range of volumes and you may find your pitch problem disappears.
3. Listen carefully.
Make sure you are actively listening as you sing. It’s easy to “turn off” your ears when you start to sing and this makes it harder to auto-adjust your pitch.
Put aside the tuner if you’re using one. Try just singing some long notes and listening as you sing. Try to judge for yourself whether the pitch is steady. This increased awareness should help you improve pitch consistency and in time it will become subconscious.
Try each of these 3 suggestions and you should be able to pinpoint the source of your singing pitch problem and fix it.