The investigators study aims are:

1. To investigate folate, vitamin B12, and homocysteine levels in patients with schizophrenia.
2. To evaluate the relationships among folate, vitamin B12, and homocysteine levels, genetic variants of one-carbon cycle pathway, psychopathology, including positive symptoms, negative symptoms, and cognition, and metabolic abnormalities in patients with schizophrenia.
3. For patients with low folate levels, the investigators would like to conduct a 24-week double-blinded, placebo-controlled of folic acid (5 mg/d) and vitamin B12 (500 ug/d) supplementation study to know whether combination of folic acid and vitamin B12 can improve patients' psychopathology or metabolic profiles, and the effects of genetic variants in one-carbon cycle pathway on treatment response.

Inclusion Criteria:

1. Age 20-65 year-old.
2. Fulfill DSM-IV-TR diagnosis of schizophrenia.
3. Be treated with an antipsychotic agent for at least 6 months or at a stable dose for at least 3 months.
4. Patients with folate deficiency or insufficiency, and PANSS score at least 60 or more in the first phase screening.

Folate deficiency and insufficiency (low folate level) are defined as serum folate < 6.8 nmol/L (3 ng/mL) and <= 13.5 nmol/L (6 ng/mL), respectively.

Exclusion Criteria:

1. Medically unstable.
2. Currently taking vitamin supplementation.
3. Pregnancy or lactation.
4. Test positive of urine drug screen
5. Megaloblastic anemia due to folate deficiency;
6. Patients with parkinsonism (score of > 12 on the Simpson-Angus Scale);
7. History of alcohol or other substances use disorder in past 3 months;
8. History of significant neurological illness;
9. Creatine>1.4 ng/dl.