How to Whiten Clothes Without Bleach

Citrus Juice
Bring a pot of water to a boil, add some slices of lemon and your clothing. Boil till the water bubbles, then take it off the heat and let it sit for about an hour.

An easier option is to just add lemon juice to your regular wash cycle.
White Vinegar – when washing your white clothes on a regular wash cycle, add half a cup of white vinegar along with your laundry detergent.

Vinegar might leave a scent after the wash cycle but it will dissipate after drying. White vinegar can also be used to treat spot stains and underarm sweat stains and smell.

Baking Soda
If you’ve got tough stains on your white clothes, you can pretreat the stains by applying a mix of baking soda and lemon juice directly onto the affected area. You can prepare a baking soda soak. Mix four litres of water with a cup of baking soda. Submerge your white shirt or other whites and let it soak for some time. One more option is to add half a cup of baking soda to your regular detergent and launder the clothes as usual.

Dishwashing Liquid
Mix 1/4 cup of it with your regular laundry detergent. Then wash your whites on a regular cycle in the washing machine.